LMFDB - Embedded newform 875.2.bb.a.143.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			143.3
Character	$\chi$	$=$	875.143
Dual form			875.2.bb.a.257.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.109427 - 2.08800i) q^{2} +(0.645540 + 0.522748i) q^{3} +(-2.35872 + 0.247911i) q^{4} +(1.02086 - 1.40509i) q^{6} +(2.15744 - 1.53148i) q^{7} +(0.121581 + 0.767632i) q^{8} +(-0.480279 - 2.25953i) q^{9} +(1.02734 + 0.218367i) q^{11} +(-1.65224 - 1.07298i) q^{12} +(2.08008 + 4.08239i) q^{13} +(-3.43382 - 4.33715i) q^{14} +(-3.05026 + 0.648353i) q^{16} +(-2.10566 - 0.808289i) q^{17} +(-4.66535 + 1.25008i) q^{18} +(0.520869 - 4.95574i) q^{19} +(2.19329 + 0.139164i) q^{21} +(0.343531 - 2.16897i) q^{22} +(6.21536 - 0.325733i) q^{23} +(-0.322792 + 0.559093i) q^{24} +(8.29642 - 4.78994i) q^{26} +(2.00245 - 3.93004i) q^{27} +(-4.70913 + 4.14720i) q^{28} +(0.743348 + 1.02313i) q^{29} +(-4.14336 - 9.30613i) q^{31} +(2.08985 + 7.79943i) q^{32} +(0.549035 + 0.678002i) q^{33} +(-1.45729 + 4.48507i) q^{34} +(1.69301 + 5.21054i) q^{36} +(-3.42368 + 5.27200i) q^{37} +(-10.4046 - 0.545281i) q^{38} +(-0.791286 + 3.72271i) q^{39} +(5.32280 + 1.72948i) q^{41} +(0.0505673 - 4.59482i) q^{42} +(-4.80861 - 4.80861i) q^{43} +(-2.47733 - 0.260378i) q^{44} +(-1.36026 - 12.9420i) q^{46} +(0.112172 + 0.292218i) q^{47} +(-2.30799 - 1.17598i) q^{48} +(2.30911 - 6.60818i) q^{49} +(-0.936759 - 1.62251i) q^{51} +(-5.91841 - 9.11355i) q^{52} +(-0.176281 + 0.217690i) q^{53} +(-8.42504 - 3.75107i) q^{54} +(1.43792 + 1.46992i) q^{56} +(2.92684 - 2.92684i) q^{57} +(2.05495 - 1.66407i) q^{58} +(-4.60084 - 5.10975i) q^{59} +(-3.94111 - 3.54859i) q^{61} +(-18.9778 + 9.66967i) q^{62} +(-4.49661 - 4.13927i) q^{63} +(10.1249 - 3.28979i) q^{64} +(1.35559 - 1.22058i) q^{66} +(-4.40181 + 11.4671i) q^{67} +(5.16706 + 1.38451i) q^{68} +(4.18254 + 3.03879i) q^{69} +(-1.66579 + 1.21027i) q^{71} +(1.67610 - 0.643393i) q^{72} +(-1.08702 + 0.705919i) q^{73} +(11.3826 + 6.57173i) q^{74} +11.8183i q^{76} +(2.55084 - 1.10223i) q^{77} +(7.85959 + 1.24484i) q^{78} +(-4.40735 + 9.89907i) q^{79} +(-2.98382 + 1.32848i) q^{81} +(3.02870 - 11.3033i) q^{82} +(3.66064 - 0.579789i) q^{83} +(-5.20787 + 0.215495i) q^{84} +(-9.51417 + 10.5666i) q^{86} +(-0.0549787 + 1.04906i) q^{87} +(-0.0427210 + 0.815165i) q^{88} +(7.09604 - 7.88095i) q^{89} +(10.7398 + 5.62191i) q^{91} +(-14.5795 + 2.30917i) q^{92} +(2.19006 - 8.17341i) q^{93} +(0.597877 - 0.266192i) q^{94} +(-2.72805 + 6.12730i) q^{96} +(4.89604 + 0.775456i) q^{97} +(-14.0505 - 4.09830i) q^{98} -2.42618i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.109427	−	2.08800i	−0.0773768	−	1.47644i	−0.711216	−	0.702973i	$-0.751855\pi$
$2$	−0.109427	−	2.08800i	−0.0773768	−	1.47644i	0.633839	−	0.773465i	$-0.281478\pi$
$3$	0.645540	+	0.522748i	0.372703	+	0.301809i	0.797311	−	0.603568i	$-0.206255\pi$
$3$	0.645540	+	0.522748i	0.372703	+	0.301809i	−0.424609	+	0.905377i	$0.639588\pi$
$4$	−2.35872	+	0.247911i	−1.17936	+	0.123956i
$5$		0			0
$5$		0			0
$6$	1.02086	−	1.40509i	0.416763	−	0.573625i
$7$	2.15744	−	1.53148i	0.815436	−	0.578847i
$7$	2.15744	−	1.53148i	0.815436	−	0.578847i
$8$	0.121581	+	0.767632i	0.0429853	+	0.271399i
$9$	−0.480279	−	2.25953i	−0.160093	−	0.753178i
$10$		0			0
$11$	1.02734	+	0.218367i	0.309753	+	0.0658401i	0.360166	−	0.932888i	$-0.382720\pi$
$11$	1.02734	+	0.218367i	0.309753	+	0.0658401i	−0.0504122	+	0.998728i	$0.516054\pi$
$12$	−1.65224	−	1.07298i	−0.476961	−	0.309742i
$13$	2.08008	+	4.08239i	0.576911	+	1.13225i	0.976492	+	0.215554i	$0.0691558\pi$
$13$	2.08008	+	4.08239i	0.576911	+	1.13225i	−0.399580	+	0.916698i	$0.630844\pi$
$14$	−3.43382	−	4.33715i	−0.917727	−	1.15915i
$15$		0			0
$16$	−3.05026	+	0.648353i	−0.762565	+	0.162088i
$17$	−2.10566	−	0.808289i	−0.510699	−	0.196039i	0.0893531	−	0.996000i	$-0.471520\pi$
$17$	−2.10566	−	0.808289i	−0.510699	−	0.196039i	−0.600052	+	0.799961i	$0.704853\pi$
$18$	−4.66535	+	1.25008i	−1.09963	+	0.294646i
$19$	0.520869	−	4.95574i	0.119496	−	1.13692i	−0.756294	−	0.654232i	$-0.772992\pi$
$19$	0.520869	−	4.95574i	0.119496	−	1.13692i	0.875790	−	0.482693i	$-0.160341\pi$
$20$		0			0
$21$	2.19329	+	0.139164i	0.478616	+	0.0303680i
$22$	0.343531	−	2.16897i	0.0732411	−	0.462426i
$23$	6.21536	−	0.325733i	1.29599	−	0.0679201i	0.608174	−	0.793804i	$-0.291902\pi$
$23$	6.21536	−	0.325733i	1.29599	−	0.0679201i	0.687818	+	0.725884i	$0.258569\pi$
$24$	−0.322792	+	0.559093i	−0.0658897	+	0.114124i
$25$		0			0
$26$	8.29642	−	4.78994i	1.62706	−	0.939384i
$27$	2.00245	−	3.93004i	0.385373	−	0.756336i
$28$	−4.70913	+	4.14720i	−0.889942	+	0.783747i
$29$	0.743348	+	1.02313i	0.138036	+	0.189991i	0.872439	−	0.488724i	$-0.162537\pi$
$29$	0.743348	+	1.02313i	0.138036	+	0.189991i	−0.734402	+	0.678714i	$0.762537\pi$
$30$		0			0
$31$	−4.14336	−	9.30613i	−0.744169	−	1.67143i	−0.741063	−	0.671435i	$-0.765678\pi$
$31$	−4.14336	−	9.30613i	−0.744169	−	1.67143i	−0.00310567	−	0.999995i	$-0.500989\pi$
$32$	2.08985	+	7.79943i	0.369437	+	1.37876i
$33$	0.549035	+	0.678002i	0.0955748	+	0.118025i
$34$	−1.45729	+	4.48507i	−0.249923	+	0.769184i
$35$		0			0
$36$	1.69301	+	5.21054i	0.282168	+	0.868424i
$37$	−3.42368	+	5.27200i	−0.562849	+	0.866712i	−0.999457	−	0.0329402i	$-0.989513\pi$
$37$	−3.42368	+	5.27200i	−0.562849	+	0.866712i	0.436608	+	0.899652i	$0.356180\pi$
$38$	−10.4046	−	0.545281i	−1.68785	−	0.0884562i
$39$	−0.791286	+	3.72271i	−0.126707	+	0.596110i
$40$		0			0
$41$	5.32280	+	1.72948i	0.831282	+	0.270100i	0.693585	−	0.720374i	$-0.256030\pi$
$41$	5.32280	+	1.72948i	0.831282	+	0.270100i	0.137697	+	0.990474i	$0.456030\pi$
$42$	0.0505673	−	4.59482i	0.00780270	−	0.708997i
$43$	−4.80861	−	4.80861i	−0.733306	−	0.733306i	0.237968	−	0.971273i	$-0.423519\pi$
$43$	−4.80861	−	4.80861i	−0.733306	−	0.733306i	−0.971273	+	0.237968i	$0.923519\pi$
$44$	−2.47733	−	0.260378i	−0.373472	−	0.0392535i
$45$		0			0
$46$	−1.36026	−	12.9420i	−0.200559	−	1.90820i
$47$	0.112172	+	0.292218i	0.0163620	+	0.0426244i	0.941518	−	0.336962i	$-0.109400\pi$
$47$	0.112172	+	0.292218i	0.0163620	+	0.0426244i	−0.925156	+	0.379587i	$0.876066\pi$
$48$	−2.30799	−	1.17598i	−0.333130	−	0.169738i
$49$	2.30911	−	6.60818i	0.329873	−	0.944025i
$50$		0			0
$51$	−0.936759	−	1.62251i	−0.131172	−	0.227197i
$52$	−5.91841	−	9.11355i	−0.820736	−	1.26382i
$53$	−0.176281	+	0.217690i	−0.0242141	+	0.0299020i	−0.789109	−	0.614253i	$-0.789457\pi$
$53$	−0.176281	+	0.217690i	−0.0242141	+	0.0299020i	0.764895	+	0.644155i	$0.222791\pi$
$54$	−8.42504	−	3.75107i	−1.14650	−	0.510456i
$55$		0			0
$56$	1.43792	+	1.46992i	0.192150	+	0.196426i
$57$	2.92684	−	2.92684i	0.387670	−	0.387670i
$58$	2.05495	−	1.66407i	0.269829	−	0.218503i
$59$	−4.60084	−	5.10975i	−0.598978	−	0.665232i	0.365064	−	0.930982i	$-0.381047\pi$
$59$	−4.60084	−	5.10975i	−0.598978	−	0.665232i	−0.964042	+	0.265750i	$0.914380\pi$
$60$		0			0
$61$	−3.94111	−	3.54859i	−0.504607	−	0.454350i	0.377083	−	0.926180i	$-0.376927\pi$
$61$	−3.94111	−	3.54859i	−0.504607	−	0.454350i	−0.881690	+	0.471829i	$0.843594\pi$
$62$	−18.9778	+	9.66967i	−2.41018	+	1.22805i
$63$	−4.49661	−	4.13927i	−0.566520	−	0.521499i
$64$	10.1249	−	3.28979i	1.26562	−	0.411224i
$65$		0			0
$66$	1.35559	−	1.22058i	0.166861	−	0.150243i
$67$	−4.40181	+	11.4671i	−0.537767	+	1.40093i	0.348304	+	0.937382i	$0.386758\pi$
$67$	−4.40181	+	11.4671i	−0.537767	+	1.40093i	−0.886071	+	0.463550i	$0.846575\pi$
$68$	5.16706	+	1.38451i	0.626598	+	0.167896i
$69$	4.18254	+	3.03879i	0.503518	+	0.365827i
$70$		0			0
$71$	−1.66579	+	1.21027i	−0.197693	+	0.143632i	−0.682228	−	0.731140i	$-0.738989\pi$
$71$	−1.66579	+	1.21027i	−0.197693	+	0.143632i	0.484535	+	0.874772i	$0.338989\pi$
$72$	1.67610	−	0.643393i	0.197530	−	0.0758246i
$73$	−1.08702	+	0.705919i	−0.127226	+	0.0826215i	−0.606683	−	0.794944i	$-0.707500\pi$
$73$	−1.08702	+	0.705919i	−0.127226	+	0.0826215i	0.479457	+	0.877565i	$0.340834\pi$
$74$	11.3826	+	6.57173i	1.32320	+	0.763948i
$75$		0			0
$76$			11.8183i			1.35566i
$77$	2.55084	−	1.10223i	0.290696	−	0.125611i
$78$	7.85959	+	1.24484i	0.889924	+	0.140950i
$79$	−4.40735	+	9.89907i	−0.495865	+	1.11373i	0.476267	+	0.879301i	$0.341989\pi$
$79$	−4.40735	+	9.89907i	−0.495865	+	1.11373i	−0.972133	+	0.234431i	$0.924677\pi$
$80$		0			0
$81$	−2.98382	+	1.32848i	−0.331536	+	0.147609i
$82$	3.02870	−	11.3033i	0.334464	−	1.24824i
$83$	3.66064	−	0.579789i	0.401808	−	0.0636401i	0.0477399	−	0.998860i	$-0.484798\pi$
$83$	3.66064	−	0.579789i	0.401808	−	0.0636401i	0.354068	+	0.935220i	$0.384798\pi$
$84$	−5.20787	+	0.215495i	−0.568225	+	0.0235124i
$85$		0			0
$86$	−9.51417	+	10.5666i	−1.02594	+	1.13942i
$87$	−0.0549787	+	1.04906i	−0.00589433	+	0.112471i
$88$	−0.0427210	+	0.815165i	−0.00455407	+	0.0868968i
$89$	7.09604	−	7.88095i	0.752179	−	0.835379i	−0.238565	−	0.971127i	$-0.576677\pi$
$89$	7.09604	−	7.88095i	0.752179	−	0.835379i	0.990743	+	0.135747i	$0.0433435\pi$
$90$		0			0
$91$	10.7398	+	5.62191i	1.12584	+	0.589337i
$92$	−14.5795	+	2.30917i	−1.52002	+	0.240748i
$93$	2.19006	−	8.17341i	0.227098	−	0.847543i
$94$	0.597877	−	0.266192i	0.0616663	−	0.0274556i
$95$		0			0
$96$	−2.72805	+	6.12730i	−0.278431	+	0.625365i
$97$	4.89604	+	0.775456i	0.497117	+	0.0787356i	0.399958	−	0.916533i	$-0.369025\pi$
$97$	4.89604	+	0.775456i	0.497117	+	0.0787356i	0.0971587	+	0.995269i	$0.469025\pi$
$98$	−14.0505	−	4.09830i	−1.41932	−	0.413991i
$99$		−	2.42618i		−	0.243840i
$100$		0			0
$101$	13.1637	+	7.60006i	1.30984	+	0.756234i	0.982069	−	0.188524i	$-0.0603704\pi$
$101$	13.1637	+	7.60006i	1.30984	+	0.756234i	0.327767	+	0.944758i	$0.393704\pi$
$102$	−3.28530	+	2.13350i	−0.325293	+	0.211248i
$103$	6.33830	−	2.43305i	0.624532	−	0.239735i	−0.0254609	−	0.999676i	$-0.508105\pi$
$103$	6.33830	−	2.43305i	0.624532	−	0.239735i	0.649993	+	0.759941i	$0.274772\pi$
$104$	−2.88088	+	2.09308i	−0.282493	+	0.205243i
$105$		0			0
$106$	0.473825	+	0.344254i	0.0460220	+	0.0334369i
$107$	18.9985	+	5.09063i	1.83665	+	0.492130i	0.998572	−	0.0534166i	$-0.0170111\pi$
$107$	18.9985	+	5.09063i	1.83665	+	0.492130i	0.838081	+	0.545546i	$0.183678\pi$
$108$	−3.74893	+	9.76629i	−0.360741	+	0.939762i
$109$	−14.2080	+	12.7930i	−1.36088	+	1.22535i	−0.411428	+	0.911442i	$0.634970\pi$
$109$	−14.2080	+	12.7930i	−1.36088	+	1.22535i	−0.949455	+	0.313903i	$0.898363\pi$
$110$		0			0
$111$	−4.96605	+	1.61357i	−0.471356	+	0.153153i
$112$	−5.58782	+	6.07021i	−0.527999	+	0.573581i
$113$	7.77652	−	3.96233i	0.731553	−	0.372745i	−0.0481952	−	0.998838i	$-0.515347\pi$
$113$	7.77652	−	3.96233i	0.731553	−	0.372745i	0.779748	+	0.626093i	$0.215347\pi$
$114$	−6.43152	−	5.79097i	−0.602367	−	0.542374i
$115$		0			0
$116$	−2.00700	−	2.22900i	−0.186345	−	0.206957i
$117$	8.22529	−	6.66071i	0.760428	−	0.615783i
$118$	−10.1657	+	10.1657i	−0.935827	+	0.935827i
$119$	−5.78073	+	1.48096i	−0.529919	+	0.135759i
$120$		0			0
$121$	−9.04127	−	4.02543i	−0.821933	−	0.365948i
$122$	−6.97819	+	8.61734i	−0.631775	+	0.780177i
$123$	2.53200	+	3.89893i	0.228303	+	0.351555i
$124$	12.0801	+	20.9234i	1.08483	+	1.87897i
$125$		0			0
$126$	−8.15074	+	9.84188i	−0.726126	+	0.876784i
$127$	11.5760	+	5.89827i	1.02720	+	0.523386i	0.884579	−	0.466390i	$-0.154446\pi$
$127$	11.5760	+	5.89827i	1.02720	+	0.523386i	0.142625	+	0.989777i	$0.454446\pi$
$128$	−2.18971	−	5.70438i	−0.193544	−	0.504201i
$129$	−0.590458	−	5.61783i	−0.0519869	−	0.494623i
$130$		0			0
$131$	3.52330	+	0.370314i	0.307832	+	0.0323545i	0.257185	−	0.966362i	$-0.417205\pi$
$131$	3.52330	+	0.370314i	0.307832	+	0.0323545i	0.0506472	+	0.998717i	$0.483872\pi$
$132$	−1.46310	−	1.46310i	−0.127347	−	0.127347i
$133$	−6.46590	−	11.4894i	−0.560664	−	0.996260i
$134$	24.4250	+	7.93617i	2.11000	+	0.685580i
$135$		0			0
$136$	0.364459	−	1.71465i	0.0312521	−	0.147030i
$137$	7.56424	+	0.396425i	0.646257	+	0.0338689i	0.372649	−	0.927972i	$-0.378450\pi$
$137$	7.56424	+	0.396425i	0.646257	+	0.0338689i	0.273608	+	0.961841i	$0.411783\pi$
$138$	5.88731	−	9.06566i	0.501161	−	0.771720i
$139$	2.73221	+	8.40888i	0.231743	+	0.713232i	0.997537	+	0.0701455i	$0.0223463\pi$
$139$	2.73221	+	8.40888i	0.231743	+	0.713232i	−0.765794	+	0.643086i	$0.777654\pi$
$140$		0			0
$141$	−0.0803449	+	0.247276i	−0.00676626	+	0.0208244i
$142$	2.70932	+	3.34573i	0.227361	+	0.280767i
$143$	1.24548	+	4.64821i	0.104153	+	0.388703i
$144$	2.92995	+	6.58078i	0.244163	+	0.548398i
$145$		0			0
$146$	1.59291	+	2.19245i	0.131830	+	0.181448i
$147$	4.94503	−	3.05876i	0.407859	−	0.252282i
$148$	6.76851	−	13.2839i	0.556368	−	1.09193i
$149$	1.52475	−	0.880317i	0.124913	−	0.0721183i	−0.436242	−	0.899830i	$-0.643691\pi$
$149$	1.52475	−	0.880317i	0.124913	−	0.0721183i	0.561154	+	0.827711i	$0.310357\pi$
$150$		0			0
$151$	−3.13479	+	5.42962i	−0.255106	+	0.441856i	−0.964924	−	0.262529i	$-0.915444\pi$
$151$	−3.13479	+	5.42962i	−0.255106	+	0.441856i	0.709819	+	0.704385i	$0.248777\pi$
$152$	3.86751	−	0.202688i	0.313697	−	0.0164401i
$153$	−0.815050	+	5.14602i	−0.0658929	+	0.416031i
$154$	−2.58060	−	5.20554i	−0.207950	−	0.419474i
$155$		0			0
$156$	0.943520	−	8.97699i	0.0755420	−	0.718735i
$157$	−10.4389	+	2.79709i	−0.833115	+	0.223232i	−0.650072	−	0.759872i	$-0.725261\pi$
$157$	−10.4389	+	2.79709i	−0.833115	+	0.223232i	−0.183043	+	0.983105i	$0.558595\pi$
$158$	21.1515	+	8.11931i	1.68272	+	0.645937i
$159$	−0.227593	+	0.0483765i	−0.0180493	+	0.00383650i
$160$		0			0
$161$	12.9104	−	10.2215i	1.01748	−	0.805565i
$162$	3.10038	+	6.08485i	0.243589	+	0.478071i
$163$	4.67900	+	3.03858i	0.366488	+	0.238000i	0.714724	−	0.699407i	$-0.246552\pi$
$163$	4.67900	+	3.03858i	0.366488	+	0.238000i	−0.348236	+	0.937407i	$0.613219\pi$
$164$	−12.9838	−	2.75978i	−1.01386	−	0.215503i
$165$		0			0
$166$	−1.61117	−	7.57998i	−0.125051	−	0.588320i
$167$	−1.64024	−	10.3561i	−0.126926	−	0.801379i	−0.966223	−	0.257706i	$-0.917033\pi$
$167$	−1.64024	−	10.3561i	−0.126926	−	0.801379i	0.839297	−	0.543673i	$-0.182967\pi$
$168$	0.159836	+	1.70056i	0.0123316	+	0.131201i
$169$	−4.69799	+	6.46623i	−0.361384	+	0.497402i
$170$		0			0
$171$	−11.4478	+	1.20322i	−0.875437	+	0.0920122i
$172$	12.5343	+	10.1500i	0.955729	+	0.773934i
$173$	0.718462	+	13.7091i	0.0546236	+	1.04228i	0.879177	+	0.476496i	$0.158093\pi$
$173$	0.718462	+	13.7091i	0.0546236	+	1.04228i	−0.824553	+	0.565785i	$0.808573\pi$
$174$	2.19644			0.166512
$175$		0			0
$176$	−3.27522			−0.246879
$177$	−0.298914	−	5.70362i	−0.0224678	−	0.428710i
$178$	−17.2319	−	13.9541i	−1.29159	−	1.04591i
$179$	−1.60078	+	0.168248i	−0.119648	+	0.0125755i	−0.164163	−	0.986433i	$-0.552492\pi$
$179$	−1.60078	+	0.168248i	−0.119648	+	0.0125755i	0.0445154	+	0.999009i	$0.485826\pi$
$180$		0			0
$181$	−2.04450	+	2.81402i	−0.151967	+	0.209164i	−0.878212	−	0.478271i	$-0.841264\pi$
$181$	−2.04450	+	2.81402i	−0.151967	+	0.209164i	0.726245	+	0.687436i	$0.241264\pi$
$182$	10.5633	−	23.0398i	0.783005	−	1.70783i
$183$	−0.689125	−	4.35096i	−0.0509416	−	0.321632i
$184$	1.00571	+	4.73150i	0.0741421	+	0.348811i
$185$		0			0
$186$	−17.3057	−	3.67844i	−1.26892	−	0.269717i
$187$	−1.98672	−	1.29019i	−0.145283	−	0.0943481i
$188$	−0.337027	−	0.661452i	−0.0245802	−	0.0482414i
$189$	−1.69861	−	11.5456i	−0.123556	−	0.839816i
$190$		0			0
$191$	2.89987	−	0.616386i	0.209827	−	0.0446001i	−0.101799	−	0.994805i	$-0.532460\pi$
$191$	2.89987	−	0.616386i	0.209827	−	0.0446001i	0.311626	+	0.950205i	$0.399126\pi$
$192$	8.25579	+	3.16910i	0.595810	+	0.228710i
$193$	16.4661	−	4.41207i	1.18525	−	0.317588i	0.388246	−	0.921556i	$-0.373081\pi$
$193$	16.4661	−	4.41207i	1.18525	−	0.317588i	0.797009	+	0.603968i	$0.206414\pi$
$194$	1.08339	−	10.3078i	0.0777829	−	0.740055i
$195$		0			0
$196$	−3.80830	+	16.1593i	−0.272022	+	1.15424i
$197$	−3.02785	+	19.1171i	−0.215725	+	1.36204i	0.607499	+	0.794320i	$0.292173\pi$
$197$	−3.02785	+	19.1171i	−0.215725	+	1.36204i	−0.823225	+	0.567716i	$0.807827\pi$
$198$	−5.06585	+	0.265490i	−0.360015	+	0.0188676i
$199$	0.0959424	−	0.166177i	0.00680118	−	0.0117800i	−0.862605	−	0.505878i	$-0.831168\pi$
$199$	0.0959424	−	0.166177i	0.00680118	−	0.0117800i	0.869406	+	0.494098i	$0.164502\pi$
$200$		0			0
$201$	−8.83596	+	5.10144i	−0.623240	+	0.359828i
$202$	14.4284	−	28.3174i	1.01518	−	1.99241i
$203$	3.17064	+	1.06892i	0.222535	+	0.0750234i
$204$	2.61179	+	3.59482i	0.182862	+	0.251688i
$205$		0			0
$206$	−5.77378	−	12.9681i	−0.402278	−	0.903532i
$207$	−3.72111	−	13.8874i	−0.258635	−	0.965239i
$208$	−8.99163	−	11.1037i	−0.623457	−	0.769906i
$209$	1.61728	−	4.97747i	0.111869	−	0.344299i
$210$		0			0
$211$	1.96658	+	6.05250i	0.135385	+	0.416671i	0.995650	−	0.0931759i	$-0.0297019\pi$
$211$	1.96658	+	6.05250i	0.135385	+	0.416671i	−0.860265	+	0.509847i	$0.829702\pi$
$212$	0.361831	−	0.557171i	0.0248507	−	0.0382666i
$213$	−1.70800	−	0.0895123i	−0.117030	−	0.00613328i
$214$	8.55027	−	40.2259i	0.584485	−	2.74978i
$215$		0			0
$216$	3.26028	+	1.05933i	0.221834	+	0.0720783i
$217$	−23.1912	−	13.7319i	−1.57432	−	0.932185i
$218$	28.2665	+	28.2665i	1.91445	+	1.91445i
$219$	−1.07073	−	0.112538i	−0.0723533	−	0.00760464i
$220$		0			0
$221$	−1.08020	−	10.2775i	−0.0726624	−	0.691337i
$222$	3.91254	+	10.1925i	0.262593	+	0.684078i
$223$	11.8807	+	6.05349i	0.795587	+	0.405372i	0.804027	−	0.594592i	$-0.202687\pi$
$223$	11.8807	+	6.05349i	0.795587	+	0.405372i	−0.00843996	+	0.999964i	$0.502687\pi$
$224$	16.4534	+	13.6262i	1.09934	+	0.910441i
$225$		0			0
$226$	−9.12431	−	15.8038i	−0.606940	−	1.05125i
$227$	−2.64274	−	4.06947i	−0.175405	−	0.270100i	0.740023	−	0.672581i	$-0.234815\pi$
$227$	−2.64274	−	4.06947i	−0.175405	−	0.270100i	−0.915428	+	0.402481i	$0.868148\pi$
$228$	−6.17801	+	7.62920i	−0.409149	+	0.505256i
$229$	6.10856	+	2.71971i	0.403665	+	0.179723i	0.598518	−	0.801109i	$-0.295756\pi$
$229$	6.10856	+	2.71971i	0.403665	+	0.179723i	−0.194853	+	0.980832i	$0.562423\pi$
$230$		0			0
$231$	2.22286	+	0.621911i	0.146254	+	0.0409187i
$232$	−0.695011	+	0.695011i	−0.0456297	+	0.0456297i
$233$	−6.71012	+	5.43374i	−0.439594	+	0.355976i	−0.823423	−	0.567428i	$-0.807939\pi$
$233$	−6.71012	+	5.43374i	−0.439594	+	0.355976i	0.383829	+	0.923404i	$0.374605\pi$
$234$	−14.8076	−	16.4455i	−0.968004	−	1.07508i
$235$		0			0
$236$	12.1189	+	10.9119i	0.788870	+	0.710302i
$237$	−8.01983	+	4.08631i	−0.520944	+	0.265434i
$238$	3.72480	+	11.9081i	0.241443	+	0.771887i
$239$	18.2461	−	5.92852i	1.18024	−	0.383484i	0.347785	−	0.937574i	$-0.386934\pi$
$239$	18.2461	−	5.92852i	1.18024	−	0.383484i	0.832457	+	0.554090i	$0.186934\pi$
$240$		0			0
$241$	19.2863	−	17.3654i	1.24234	−	1.11861i	0.253861	−	0.967241i	$-0.418300\pi$
$241$	19.2863	−	17.3654i	1.24234	−	1.11861i	0.988478	−	0.151366i	$-0.0483671\pi$
$242$	−7.41573	+	19.3186i	−0.476701	+	1.24185i
$243$	−15.4021	−	4.12698i	−0.988046	−	0.264746i
$244$	10.1757	+	7.39308i	0.651433	+	0.473294i
$245$		0			0
$246$	7.86390	−	5.71346i	0.501384	−	0.364277i
$247$	21.3147	−	8.18196i	1.35622	−	0.520606i
$248$	6.63993	−	4.31202i	0.421636	−	0.273814i
$249$	2.66617	+	1.53932i	0.168962	+	0.0975502i
$250$		0			0
$251$		−	15.4133i		−	0.972880i	−0.873714	−	0.486440i	$-0.838295\pi$
$251$		−	15.4133i		−	0.972880i	0.873714	−	0.486440i	$-0.161705\pi$
$252$	11.6324	+	8.64862i	0.732774	+	0.544812i
$253$	6.45639	+	1.02259i	0.405910	+	0.0642898i
$254$	11.0488	−	24.8161i	0.693266	−	1.55710i
$255$		0			0
$256$	7.78009	−	3.46392i	0.486256	−	0.216495i
$257$	−7.91188	+	29.5275i	−0.493529	+	1.84188i	0.0445856	+	0.999006i	$0.485803\pi$
$257$	−7.91188	+	29.5275i	−0.493529	+	1.84188i	−0.538115	+	0.842871i	$0.680863\pi$
$258$	−11.6654	+	1.84762i	−0.726257	+	0.115028i
$259$	0.687603	+	16.6173i	0.0427256	+	1.03255i
$260$		0			0
$261$	1.95479	−	2.17101i	0.120998	−	0.134382i
$262$	0.387670	−	7.39718i	0.0239503	−	0.456999i
$263$	−0.0213379	+	0.407151i	−0.00131575	+	0.0251060i	−0.999209	−	0.0397788i	$-0.987335\pi$
$263$	−0.0213379	+	0.407151i	−0.00131575	+	0.0251060i	0.997893	+	0.0648848i	$0.0206680\pi$
$264$	−0.453704	+	0.503889i	−0.0279235	+	0.0310122i
$265$		0			0
$266$	−23.2824	+	14.7580i	−1.42753	+	0.904873i
$267$	8.70053	−	1.37803i	0.532464	−	0.0843340i
$268$	7.53982	−	28.1390i	0.460568	−	1.71886i
$269$	−17.4978	+	7.79051i	−1.06686	+	0.474996i	−0.863625	−	0.504134i	$-0.831812\pi$
$269$	−17.4978	+	7.79051i	−1.06686	+	0.474996i	−0.203233	+	0.979130i	$0.565145\pi$
$270$		0			0
$271$	−7.85265	+	17.6373i	−0.477015	+	1.07139i	0.501489	+	0.865164i	$0.332786\pi$
$271$	−7.85265	+	17.6373i	−0.477015	+	1.07139i	−0.978504	+	0.206228i	$0.933881\pi$
$272$	6.94688	+	1.10028i	0.421216	+	0.0667141i
$273$	3.99411	+	9.24337i	0.241735	+	0.559434i
$274$		−	15.8375i		−	0.956779i
$275$		0			0
$276$	−10.6188	−	6.13076i	−0.639176	−	0.369028i
$277$	6.41377	−	4.16515i	0.385366	−	0.250260i	−0.337387	−	0.941366i	$-0.609543\pi$
$277$	6.41377	−	4.16515i	0.385366	−	0.250260i	0.722753	+	0.691106i	$0.242876\pi$
$278$	17.2587	−	6.62501i	1.03511	−	0.397342i
$279$	−19.0376	+	13.8316i	−1.13975	+	0.828076i
$280$		0			0
$281$	15.1432	+	11.0022i	0.903367	+	0.656334i	0.939329	−	0.343019i	$-0.111449\pi$
$281$	15.1432	+	11.0022i	0.903367	+	0.656334i	−0.0359618	+	0.999353i	$0.511449\pi$
$282$	0.525104	+	0.140701i	0.0312695	+	0.00837864i
$283$	1.02124	−	2.66042i	0.0607063	−	0.158145i	−0.899873	−	0.436153i	$-0.856341\pi$
$283$	1.02124	−	2.66042i	0.0607063	−	0.158145i	0.960579	+	0.278008i	$0.0896740\pi$
$284$	3.62909	−	3.26765i	0.215347	−	0.193899i
$285$		0			0
$286$	9.56917	−	3.10921i	0.565837	−	0.183852i
$287$	14.1323	−	4.42053i	0.834204	−	0.260936i
$288$	16.6194	−	8.46799i	0.979305	−	0.498981i
$289$	−8.85297	−	7.97125i	−0.520763	−	0.468897i
$290$		0			0
$291$	2.75522	+	3.05998i	0.161514	+	0.179379i
$292$	2.38897	−	1.93455i	0.139804	−	0.113211i
$293$	0.584948	−	0.584948i	0.0341730	−	0.0341730i	−0.689814	−	0.723987i	$-0.742308\pi$
$293$	0.584948	−	0.584948i	0.0341730	−	0.0341730i	0.723987	+	0.689814i	$0.242308\pi$
$294$	−6.92781	−	9.99051i	−0.404038	−	0.582658i
$295$		0			0
$296$	−4.46321	−	1.98715i	−0.259419	−	0.115501i
$297$	2.91538	−	3.60020i	0.169168	−	0.208905i
$298$	−2.00495	−	3.08735i	−0.116144	−	0.178845i
$299$	14.2582	+	24.6960i	0.824575	+	1.42821i
$300$		0			0
$301$	−17.7386	−	3.00998i	−1.02244	−	0.173492i
$302$	11.6801	+	5.95129i	0.672112	+	0.342458i
$303$	4.52477	+	11.7874i	0.259941	+	0.677170i
$304$	1.62428	+	15.4540i	0.0931589	+	0.886348i
$305$		0			0
$306$	10.8341	+	1.13871i	0.619343	+	0.0650956i
$307$	−10.4006	−	10.4006i	−0.593593	−	0.593593i	0.345007	−	0.938600i	$-0.387877\pi$
$307$	−10.4006	−	10.4006i	−0.593593	−	0.593593i	−0.938600	+	0.345007i	$0.887877\pi$
$308$	−5.74347	+	3.23225i	−0.327264	+	0.184174i
$309$	5.36350	+	1.74271i	0.305119	+	0.0991391i
$310$		0			0
$311$	−2.47049	+	11.6228i	−0.140089	+	0.659066i	0.850923	+	0.525291i	$0.176043\pi$
$311$	−2.47049	+	11.6228i	−0.140089	+	0.659066i	−0.991012	+	0.133776i	$0.957290\pi$
$312$	−2.95387	−	0.154806i	−0.167230	−	0.00876416i
$313$	−5.48632	+	8.44819i	−0.310105	+	0.477520i	−0.959019	−	0.283342i	$-0.908557\pi$
$313$	−5.48632	+	8.44819i	−0.310105	+	0.477520i	0.648914	+	0.760862i	$0.275223\pi$
$314$	6.98263	+	21.4903i	0.394053	+	1.21277i
$315$		0			0
$316$	7.94161	−	24.4418i	0.446750	−	1.37496i
$317$	11.8979	+	14.6927i	0.668252	+	0.825223i	0.992691	−	0.120684i	$-0.0385087\pi$
$317$	11.8979	+	14.6927i	0.668252	+	0.825223i	−0.324439	+	0.945907i	$0.605175\pi$
$318$	0.125915	+	0.469921i	0.00706096	+	0.0263519i
$319$	0.540250	+	1.21342i	0.0302482	+	0.0679386i
$320$		0			0
$321$	9.60316	+	13.2176i	0.535996	+	0.737736i
$322$	−22.7552	−	25.8384i	−1.26810	−	1.43992i
$323$	−5.10245	+	10.0141i	−0.283908	+	0.557200i
$324$	6.70866	−	3.87325i	0.372703	−	0.215180i
$325$		0			0
$326$	5.83254	−	10.1023i	0.323035	−	0.559512i
$327$	−15.8594	+	0.831154i	−0.877024	+	0.0459629i
$328$	−0.680455	+	4.29622i	−0.0375719	+	0.237219i
$329$	0.689532	+	0.458654i	0.0380152	+	0.0252864i
$330$		0			0
$331$	−3.25235	+	30.9441i	−0.178766	+	1.70084i	0.426232	+	0.904614i	$0.359841\pi$
$331$	−3.25235	+	30.9441i	−0.178766	+	1.70084i	−0.604998	+	0.796227i	$0.706826\pi$
$332$	−8.49070	+	2.27508i	−0.465988	+	0.124861i
$333$	13.5566	+	5.20388i	0.742896	+	0.285171i
$334$	−21.4440	+	4.55807i	−1.17336	+	0.249406i
$335$		0			0
$336$	−6.78035	+	0.997543i	−0.369898	+	0.0544204i
$337$	−15.8054	−	31.0198i	−0.860974	−	1.68976i	−0.713460	−	0.700696i	$-0.752873\pi$
$337$	−15.8054	−	31.0198i	−0.860974	−	1.68976i	−0.147514	−	0.989060i	$-0.547127\pi$
$338$	14.0156	+	9.10181i	0.762346	+	0.495073i
$339$	7.09135	+	1.50731i	0.385149	+	0.0818660i
$340$		0			0
$341$	−2.22447	−	10.4653i	−0.120462	−	0.566727i
$342$	3.76502	+	23.7714i	0.203589	+	1.28541i
$343$	−5.13855	−	17.7931i	−0.277456	−	0.960738i
$344$	3.10660	−	4.27587i	0.167497	−	0.230540i
$345$		0			0
$346$	28.5459	−	3.00029i	1.53464	−	0.161297i
$347$	−20.9357	−	16.9534i	−1.12389	−	0.910107i	−0.127237	−	0.991872i	$-0.540611\pi$
$347$	−20.9357	−	16.9534i	−1.12389	−	0.910107i	−0.996652	+	0.0817651i	$0.973944\pi$
$348$	−0.130394	−	2.48806i	−0.00698983	−	0.133374i
$349$	−28.9278			−1.54847			−0.774236	−	0.632897i	$-0.781866\pi$
$349$	−28.9278			−1.54847			−0.774236	+	0.632897i	$0.781866\pi$
$350$		0			0
$351$	20.2092			1.07869
$352$	0.443841	+	8.46898i	0.0236568	+	0.451398i
$353$	9.06748	+	7.34270i	0.482613	+	0.390813i	0.839521	−	0.543327i	$-0.182836\pi$
$353$	9.06748	+	7.34270i	0.482613	+	0.390813i	−0.356908	+	0.934140i	$0.616169\pi$
$354$	−11.8764	+	1.24826i	−0.631226	+	0.0663445i
$355$		0			0
$356$	−14.7838	+	20.3482i	−0.783540	+	1.07845i
$357$	−4.50586	−	2.06585i	−0.238475	−	0.109336i
$358$	0.526471	+	3.32401i	0.0278248	+	0.175679i
$359$	−0.925593	−	4.35457i	−0.0488509	−	0.229826i	0.946949	−	0.321385i	$-0.104148\pi$
$359$	−0.925593	−	4.35457i	−0.0488509	−	0.229826i	−0.995800	+	0.0915592i	$0.970815\pi$
$360$		0			0
$361$	−5.70326	−	1.21227i	−0.300172	−	0.0638034i
$362$	6.09939	+	3.96099i	0.320577	+	0.208185i
$363$	−3.73221	−	7.32488i	−0.195890	−	0.384456i
$364$	−26.7259	−	10.5980i	−1.40082	−	0.555486i
$365$		0			0
$366$	−9.00939	+	1.91501i	−0.470928	+	0.100099i
$367$	23.9770	+	9.20390i	1.25159	+	0.480440i	0.891730	−	0.452567i	$-0.149492\pi$
$367$	23.9770	+	9.20390i	1.25159	+	0.480440i	0.359858	+	0.933007i	$0.382825\pi$
$368$	−18.7473	+	5.02332i	−0.977269	+	0.261858i
$369$	1.35140	−	12.8577i	0.0703510	−	0.669345i
$370$		0			0
$371$	−0.0469289	+	0.739625i	−0.00243643	+	0.0383994i
$372$	−3.13945	+	19.8217i	−0.162773	+	1.02771i
$373$	−35.7641	+	1.87432i	−1.85180	+	0.0970485i	−0.945506	−	0.325606i	$-0.894432\pi$
$373$	−35.7641	+	1.87432i	−1.85180	+	0.0970485i	−0.906291	+	0.422655i	$0.861098\pi$
$374$	−2.47652	+	4.28945i	−0.128058	+	0.221802i
$375$		0			0
$376$	−0.210678	+	0.121635i	−0.0108649	+	0.00627285i
$377$	−2.63060	+	5.16284i	−0.135483	+	0.265900i
$378$	−23.9212	+	4.81010i	−1.23038	+	0.247405i
$379$	13.3436	+	18.3659i	0.685416	+	0.943394i	0.999983	−	0.00584095i	$-0.00185924\pi$
$379$	13.3436	+	18.3659i	0.685416	+	0.943394i	−0.314567	+	0.949235i	$0.601859\pi$
$380$		0			0
$381$	4.38946	+	9.85889i	0.224879	+	0.505086i
$382$	−1.60434	−	5.98747i	−0.0820850	−	0.306346i
$383$	−13.6894	−	16.9050i	−0.699496	−	0.863806i	0.296329	−	0.955086i	$-0.404237\pi$
$383$	−13.6894	−	16.9050i	−0.699496	−	0.863806i	−0.995825	+	0.0912802i	$0.970904\pi$
$384$	1.56841	−	4.82707i	0.0800375	−	0.246330i
$385$		0			0
$386$	−11.0142	−	33.8984i	−0.560610	−	1.72538i
$387$	−8.55574	+	13.1747i	−0.434913	+	0.669707i
$388$	−11.7406	−	0.615300i	−0.596040	−	0.0312371i
$389$	−2.70252	+	12.7143i	−0.137023	+	0.644643i	0.855004	+	0.518621i	$0.173554\pi$
$389$	−2.70252	+	12.7143i	−0.137023	+	0.644643i	−0.992027	+	0.126022i	$0.959779\pi$
$390$		0			0
$391$	−13.3507	−	4.33792i	−0.675176	−	0.219378i
$392$	5.35339	+	0.969118i	0.270387	+	0.0489478i
$393$	2.08085	+	2.08085i	0.104965	+	0.104965i
$394$	40.2478	+	4.23021i	2.02765	+	0.213115i
$395$		0			0
$396$	0.601477	+	5.72267i	0.0302254	+	0.287575i
$397$	−1.71242	−	4.46102i	−0.0859441	−	0.223892i	0.883872	−	0.467728i	$-0.154927\pi$
$397$	−1.71242	−	4.46102i	−0.0859441	−	0.223892i	−0.969816	+	0.243836i	$0.921594\pi$
$398$	−0.357476	−	0.182143i	−0.0179187	−	0.00913002i
$399$	1.83208	−	10.7969i	0.0917187	−	0.540522i
$400$		0			0
$401$	7.58351	+	13.1350i	0.378702	+	0.655932i	0.990874	−	0.134793i	$-0.0430370\pi$
$401$	7.58351	+	13.1350i	0.378702	+	0.655932i	−0.612171	+	0.790725i	$0.709704\pi$
$402$	11.6187	+	17.8912i	0.579488	+	0.892333i
$403$	29.3728	−	36.2724i	1.46316	−	1.80685i
$404$	−32.9336	−	14.6630i	−1.63851	−	0.729511i
$405$		0			0
$406$	1.88495	−	6.73726i	0.0935484	−	0.334365i
$407$	−4.66850	+	4.66850i	−0.231409	+	0.231409i
$408$	1.13160	−	0.916352i	0.0560226	−	0.0453662i
$409$	−6.87712	−	7.63781i	−0.340052	−	0.377666i	0.548728	−	0.836001i	$-0.315112\pi$
$409$	−6.87712	−	7.63781i	−0.340052	−	0.377666i	−0.888779	+	0.458336i	$0.848446\pi$
$410$		0			0
$411$	4.67579	+	4.21010i	0.230640	+	0.207669i
$412$	−14.3471	+	7.31021i	−0.706831	+	0.360148i
$413$	−17.7515	−	3.97787i	−0.873496	−	0.195738i
$414$	−28.5896	+	9.28933i	−1.40510	+	0.456546i
$415$		0			0
$416$	−27.4933	+	24.7551i	−1.34797	+	1.21372i
$417$	−2.63197	+	6.85652i	−0.128888	+	0.335765i
$418$	−10.5699	−	2.83220i	−0.516992	−	0.138528i
$419$	14.4852	+	10.5241i	0.707648	+	0.514137i	0.882414	−	0.470473i	$-0.155917\pi$
$419$	14.4852	+	10.5241i	0.707648	+	0.514137i	−0.174766	+	0.984610i	$0.555917\pi$
$420$		0			0
$421$	13.5865	−	9.87120i	0.662168	−	0.481093i	−0.205227	−	0.978714i	$-0.565793\pi$
$421$	13.5865	−	9.87120i	0.662168	−	0.481093i	0.867394	+	0.497621i	$0.165793\pi$
$422$	12.4224	−	4.76852i	0.604714	−	0.232128i
$423$	0.606403	−	0.393803i	0.0294843	−	0.0191473i
$424$	−0.188538	−	0.108852i	−0.00915621	−	0.00528634i
$425$		0			0
$426$			3.57609i			0.173262i
$427$	−13.9373	−	1.62013i	−0.674474	−	0.0784036i
$428$	−46.0741	−	7.29743i	−2.22708	−	0.352734i
$429$	−1.62583	+	3.65168i	−0.0784959	+	0.176305i
$430$		0			0
$431$	−8.17166	+	3.63826i	−0.393615	+	0.175249i	−0.593993	−	0.804470i	$-0.702449\pi$
$431$	−8.17166	+	3.63826i	−0.393615	+	0.175249i	0.200378	+	0.979719i	$0.435783\pi$
$432$	−3.55996	+	13.2859i	−0.171278	+	0.639220i
$433$	−17.4040	+	2.75652i	−0.836382	+	0.132470i	−0.559912	−	0.828552i	$-0.689165\pi$
$433$	−17.4040	+	2.75652i	−0.836382	+	0.132470i	−0.276471	+	0.961022i	$0.589165\pi$
$434$	−26.1345	+	49.9259i	−1.25450	+	2.39652i
$435$		0			0
$436$	30.3413	−	33.6974i	1.45308	−	1.61381i
$437$	1.62314	−	30.9714i	0.0776454	−	1.48156i
$438$	−0.117813	+	2.24800i	−0.00562931	+	0.107414i
$439$	18.3365	−	20.3647i	0.875151	−	0.971954i	−0.124644	−	0.992202i	$-0.539779\pi$
$439$	18.3365	−	20.3647i	0.875151	−	0.971954i	0.999795	+	0.0202474i	$0.00644540\pi$
$440$		0			0
$441$	−16.0404	−	2.04375i	−0.763829	−	0.0973212i
$442$	−21.3411	+	3.38010i	−1.01509	+	0.160775i
$443$	−2.86872	+	10.7062i	−0.136297	+	0.508667i	0.863692	+	0.504019i	$0.168146\pi$
$443$	−2.86872	+	10.7062i	−0.136297	+	0.508667i	−0.999989	+	0.00464732i	$0.998521\pi$
$444$	11.3135	−	5.03709i	0.536914	−	0.239050i
$445$		0			0
$446$	11.3396	−	25.4692i	0.536947	−	1.20600i
$447$	1.44447	+	0.228782i	0.0683212	+	0.0108210i
$448$	16.8057	−	22.6037i	0.793995	−	1.06793i
$449$		−	40.1154i		−	1.89316i	−0.322465	−	0.946581i	$-0.604511\pi$
$449$		−	40.1154i		−	1.89316i	0.322465	−	0.946581i	$-0.395489\pi$
$450$		0			0
$451$	5.09064	+	2.93909i	0.239709	+	0.138396i
$452$	−17.3603	+	11.2739i	−0.816561	+	0.530281i
$453$	−4.86195	+	1.86633i	−0.228434	+	0.0876878i
$454$	−8.20786	+	5.96336i	−0.385214	+	0.279874i
$455$		0			0
$456$	2.60259	+	1.89089i	0.121877	+	0.0885490i
$457$	−32.8230	−	8.79489i	−1.53539	−	0.411408i	−0.610620	−	0.791924i	$-0.709080\pi$
$457$	−32.8230	−	8.79489i	−1.53539	−	0.411408i	−0.924774	+	0.380516i	$0.875746\pi$
$458$	5.01030	−	13.0523i	0.234116	−	0.609893i
$459$	−7.39310	+	6.65678i	−0.345081	+	0.310712i
$460$		0			0
$461$	30.0506	−	9.76402i	1.39959	−	0.454756i	0.490535	−	0.871422i	$-0.336802\pi$
$461$	30.0506	−	9.76402i	1.39959	−	0.454756i	0.909060	+	0.416666i	$0.136802\pi$
$462$	1.05531	−	4.70938i	0.0490973	−	0.219100i
$463$	−16.9684	+	8.64582i	−0.788587	+	0.401805i	−0.801412	−	0.598113i	$-0.795918\pi$
$463$	−16.9684	+	8.64582i	−0.788587	+	0.401805i	0.0128250	+	0.999918i	$0.495918\pi$
$464$	−2.93076	−	2.63886i	−0.136057	−	0.122506i
$465$		0			0
$466$	12.0799	+	13.4161i	0.559592	+	0.621489i
$467$	−4.63073	+	3.74989i	−0.214285	+	0.173524i	−0.730453	−	0.682963i	$-0.760691\pi$
$467$	−4.63073	+	3.74989i	−0.214285	+	0.173524i	0.516169	+	0.856487i	$0.327358\pi$
$468$	−17.7499	+	17.7499i	−0.820489	+	0.820489i
$469$	8.06506	+	31.4810i	0.372410	+	1.45366i
$470$		0			0
$471$	−8.20090	−	3.65128i	−0.377877	−	0.168242i
$472$	3.36303	−	4.15300i	0.154796	−	0.191157i
$473$	−3.89001	−	5.99009i	−0.178863	−	0.275425i
$474$	9.40980	+	16.2982i	0.432206	+	0.748603i
$475$		0			0
$476$	13.2680	−	4.92627i	0.608137	−	0.225795i
$477$	0.576541	+	0.293762i	0.0263980	+	0.0134505i
$478$	−14.3754	−	37.4491i	−0.657513	−	1.71288i
$479$	−2.17952	−	20.7367i	−0.0995846	−	0.947484i	−0.924231	−	0.381835i	$-0.875292\pi$
$479$	−2.17952	−	20.7367i	−0.0995846	−	0.947484i	0.824646	−	0.565649i	$-0.191374\pi$
$480$		0			0
$481$	−28.6439	−	3.01060i	−1.30605	−	0.137271i
$482$	−38.3695	−	38.3695i	−1.74768	−	1.74768i
$483$	13.6774	+	0.150524i	0.622345	+	0.00684907i
$484$	22.3238	+	7.25343i	1.01472	+	0.329701i
$485$		0			0
$486$	−6.93172	+	32.6112i	−0.314429	+	1.47927i
$487$	29.3101	+	1.53608i	1.32817	+	0.0696064i	0.703171	−	0.711021i	$-0.251767\pi$
$487$	29.3101	+	1.53608i	1.32817	+	0.0696064i	0.624997	+	0.780627i	$0.285100\pi$
$488$	2.24485	−	3.45676i	0.101619	−	0.156480i
$489$	1.43207	+	4.40746i	0.0647605	+	0.199312i
$490$		0			0
$491$	−5.56395	+	17.1241i	−0.251097	+	0.772798i	0.743476	+	0.668762i	$0.233176\pi$
$491$	−5.56395	+	17.1241i	−0.251097	+	0.772798i	−0.994574	+	0.104036i	$0.966824\pi$
$492$	−6.93886	−	8.56878i	−0.312828	−	0.386311i
$493$	−0.738256	−	2.75521i	−0.0332494	−	0.124088i
$494$	−19.4163	−	43.6098i	−0.873583	−	1.96210i
$495$		0			0
$496$	18.6720	+	25.6998i	0.838396	+	1.15395i
$497$	−1.74034	+	5.16221i	−0.0780648	+	0.231557i
$498$	2.92234	−	5.73541i	0.130953	−	0.257010i
$499$	−4.60639	+	2.65950i	−0.206210	+	0.119056i	−0.599549	−	0.800338i	$-0.704653\pi$
$499$	−4.60639	+	2.65950i	−0.206210	+	0.119056i	0.393339	+	0.919394i	$0.371320\pi$
$500$		0			0
$501$	4.35478	−	7.54270i	0.194557	−	0.336983i
$502$	−32.1830	+	1.68664i	−1.43640	+	0.0752784i
$503$	−4.13001	+	26.0759i	−0.184148	+	1.16267i	0.706412	+	0.707801i	$0.250313\pi$
$503$	−4.13001	+	26.0759i	−0.184148	+	1.16267i	−0.890560	+	0.454865i	$0.849687\pi$
$504$	2.63073	−	3.95500i	0.117182	−	0.176170i
$505$		0			0
$506$	1.42866	−	13.5928i	0.0635119	−	0.604275i
$507$	−6.41294	+	1.71834i	−0.284809	+	0.0763143i
$508$	−28.7668	−	11.0425i	−1.27632	−	0.489933i
$509$	−4.37813	+	0.930600i	−0.194057	+	0.0412481i	−0.303915	−	0.952699i	$-0.598294\pi$
$509$	−4.37813	+	0.930600i	−0.194057	+	0.0412481i	0.109858	+	0.993947i	$0.464960\pi$
$510$		0			0
$511$	−1.26408	+	3.18773i	−0.0559195	+	0.141017i
$512$	−13.6320	−	26.7543i	−0.602454	−	1.18238i
$513$	−18.4332	−	11.9707i	−0.813847	−	0.528519i
$514$	62.5192	+	13.2889i	2.75760	+	0.586147i
$515$		0			0
$516$	2.78545	+	13.1045i	0.122623	+	0.576894i
$517$	0.0514276	+	0.324701i	0.00226178	+	0.0142803i
$518$	34.6217	−	3.25411i	1.52119	−	0.142977i
$519$	−6.70259	+	9.22532i	−0.294211	+	0.404947i
$520$		0			0
$521$	−25.5618	+	2.68665i	−1.11988	+	0.117704i	−0.646327	−	0.763060i	$-0.723696\pi$
$521$	−25.5618	+	2.68665i	−1.11988	+	0.117704i	−0.473554	+	0.880765i	$0.657029\pi$
$522$	−4.74697	−	3.84402i	−0.207769	−	0.168248i
$523$	1.15135	+	21.9690i	0.0503450	+	0.960639i	0.900703	+	0.434435i	$0.143052\pi$
$523$	1.15135	+	21.9690i	0.0503450	+	0.960639i	−0.850358	+	0.526204i	$0.823615\pi$
$524$	−8.40229			−0.367056
$525$		0			0
$526$	0.852467			0.0371693
$527$	1.20248	+	22.9446i	0.0523807	+	0.999483i
$528$	−2.11428	−	1.71211i	−0.0920124	−	0.0745102i
$529$	15.6506	−	1.64494i	0.680460	−	0.0715192i
$530$		0			0
$531$	−9.33596	+	12.8499i	−0.405146	+	0.557636i
$532$	18.0996	+	25.4974i	0.784717	+	1.10545i
$533$	4.01144	+	25.3273i	0.173755	+	1.09705i
$534$	−3.82940	−	18.0159i	−0.165714	−	0.779624i
$535$		0			0
$536$	−9.33770	−	1.98479i	−0.403327	−	0.0857299i
$537$	−1.12132	−	0.728191i	−0.0483883	−	0.0314238i
$538$	18.1813	+	35.6828i	0.783852	+	1.53840i
$539$	3.81524	−	6.28458i	0.164334	−	0.270696i
$540$		0			0
$541$	−7.92633	+	1.68479i	−0.340780	+	0.0724349i	−0.375123	−	0.926975i	$-0.622399\pi$
$541$	−7.92633	+	1.68479i	−0.340780	+	0.0724349i	0.0343432	+	0.999410i	$0.489066\pi$
$542$	37.6860	+	14.4663i	1.61875	+	0.621381i
$543$	−2.79083	+	0.747801i	−0.119766	+	0.0320912i
$544$	1.90367	−	18.1122i	0.0816190	−	0.776553i
$545$		0			0
$546$	18.8631	−	9.35118i	0.807265	−	0.400194i
$547$	−3.02255	+	19.0836i	−0.129235	+	0.815958i	0.834872	+	0.550444i	$0.185542\pi$
$547$	−3.02255	+	19.0836i	−0.129235	+	0.815958i	−0.964107	+	0.265514i	$0.914458\pi$
$548$	−17.9402	+	0.940206i	−0.766368	+	0.0401636i
$549$	−6.12533	+	10.6094i	−0.261423	+	0.452797i
$550$		0			0
$551$	5.45756	−	3.15092i	0.232500	−	0.134234i
$552$	−1.82416	+	3.58011i	−0.0776412	+	0.152379i
$553$	5.65167	+	28.1064i	0.240333	+	1.19521i
$554$	−9.39867	−	12.9362i	−0.399311	−	0.549605i
$555$		0			0
$556$	−8.52918	−	19.1568i	−0.361718	−	0.812431i
$557$	−4.82211	−	17.9964i	−0.204320	−	0.762531i	−0.989656	−	0.143462i	$-0.954177\pi$
$557$	−4.82211	−	17.9964i	−0.204320	−	0.762531i	0.785336	−	0.619069i	$-0.212490\pi$
$558$	30.9636	+	38.2368i	1.31079	+	1.61869i
$559$	9.62832	−	29.6329i	0.407235	−	1.25334i
$560$		0			0
$561$	−0.608062	−	1.87142i	−0.0256724	−	0.0790116i
$562$	21.3154	−	32.8229i	0.899137	−	1.38455i
$563$	21.5909	+	1.13153i	0.909947	+	0.0476883i	0.501562	−	0.865122i	$-0.332759\pi$
$563$	21.5909	+	1.13153i	0.909947	+	0.0476883i	0.408385	+	0.912810i	$0.366092\pi$
$564$	0.128209	−	0.603174i	0.00539855	−	0.0253982i
$565$		0			0
$566$	−5.66670	−	1.84122i	−0.238189	−	0.0773923i
$567$	−4.40287	+	7.43581i	−0.184903	+	0.312275i
$568$	−1.13157	−	1.13157i	−0.0474795	−	0.0474795i
$569$	−39.9222	−	4.19599i	−1.67362	−	0.175905i	−0.780327	−	0.625371i	$-0.784947\pi$
$569$	−39.9222	−	4.19599i	−1.67362	−	0.175905i	−0.893297	+	0.449466i	$0.851614\pi$
$570$		0			0
$571$	−3.48054	−	33.1151i	−0.145656	−	1.38582i	−0.786233	−	0.617930i	$-0.787971\pi$
$571$	−3.48054	−	33.1151i	−0.145656	−	1.38582i	0.640577	−	0.767894i	$-0.278695\pi$
$572$	−4.09009	−	10.6551i	−0.171015	−	0.445510i
$573$	2.19419	+	1.11800i	0.0916638	+	0.0467050i
$574$	−10.7765	−	29.0245i	−0.449803	−	1.21146i
$575$		0			0
$576$	−12.2962	−	21.2976i	−0.512342	−	0.887402i
$577$	3.12235	+	4.80800i	0.129985	+	0.200160i	0.897670	−	0.440667i	$-0.145258\pi$
$577$	3.12235	+	4.80800i	0.129985	+	0.200160i	−0.767685	+	0.640827i	$0.778592\pi$
$578$	−15.6752	+	19.3573i	−0.652002	+	0.805156i
$579$	12.9359	+	5.75944i	0.537598	+	0.239354i
$580$		0			0
$581$	7.00969	−	6.85708i	0.290811	−	0.284480i
$582$	6.08774	−	6.08774i	0.252345	−	0.252345i
$583$	−0.228636	+	0.185146i	−0.00946915	+	0.00766797i
$584$	−0.674046	−	0.748604i	−0.0278922	−	0.0309775i
$585$		0			0
$586$	−1.28538	−	1.15736i	−0.0530985	−	0.0478101i
$587$	−10.7577	+	5.48135i	−0.444020	+	0.226239i	−0.661682	−	0.749785i	$-0.730157\pi$
$587$	−10.7577	+	5.48135i	−0.444020	+	0.226239i	0.217662	+	0.976024i	$0.430157\pi$
$588$	−10.9056	+	8.44069i	−0.449741	+	0.348088i
$589$	−48.2769	+	15.6861i	−1.98922	+	0.646335i
$590$		0			0
$591$	−11.9480	+	10.7580i	−0.491475	+	0.442526i
$592$	7.02499	−	18.3007i	0.288725	−	0.752155i
$593$	−41.9372	−	11.2370i	−1.72215	−	0.461449i	−0.743802	−	0.668401i	$-0.766979\pi$
$593$	−41.9372	−	11.2370i	−1.72215	−	0.461449i	−0.978351	+	0.206951i	$0.933646\pi$
$594$	−7.83623	−	5.69336i	−0.321525	−	0.233601i
$595$		0			0
$596$	−3.37823	+	2.45442i	−0.138377	+	0.100537i
$597$	0.148803	−	0.0571202i	0.00609011	−	0.00233778i
$598$	50.0050	−	32.4736i	2.04485	−	1.32794i
$599$	0.677665	+	0.391250i	0.0276887	+	0.0159860i	0.513780	−	0.857922i	$-0.328245\pi$
$599$	0.677665	+	0.391250i	0.0276887	+	0.0159860i	−0.486092	+	0.873908i	$0.661578\pi$
$600$		0			0
$601$		−	7.23002i		−	0.294919i	−0.989068	−	0.147459i	$-0.952890\pi$
$601$		−	7.23002i		−	0.294919i	0.989068	−	0.147459i	$-0.0471095\pi$
$602$	−4.34375	+	37.3675i	−0.177038	+	1.52299i
$603$	28.0244	+	4.43864i	1.14124	+	0.180755i
$604$	6.04803	−	13.5841i	0.246091	−	0.552729i
$605$		0			0
$606$	24.1170	−	10.7376i	0.979686	−	0.436184i
$607$	0.459640	−	1.71540i	0.0186562	−	0.0696260i	−0.955970	−	0.293464i	$-0.905192\pi$
$607$	0.459640	−	1.71540i	0.0186562	−	0.0696260i	0.974626	+	0.223838i	$0.0718586\pi$
$608$	39.7405	−	6.29427i	1.61169	−	0.255267i
$609$	1.48800	+	2.34747i	0.0602968	+	0.0951245i
$610$		0			0
$611$	−0.959623	+	1.06577i	−0.0388222	+	0.0431164i
$612$	0.646717	−	12.3401i	0.0261420	−	0.498819i
$613$	−0.0573433	+	1.09418i	−0.00231608	+	0.0441934i	−0.999543	−	0.0302265i	$-0.990377\pi$
$613$	−0.0573433	+	1.09418i	−0.00231608	+	0.0441934i	0.997227	+	0.0744198i	$0.0237105\pi$
$614$	−20.5783	+	22.8545i	−0.830473	+	0.922334i
$615$		0			0
$616$	1.15624	+	1.82410i	0.0465864	+	0.0734950i
$617$	−31.8056	+	5.03752i	−1.28045	+	0.202803i	−0.759343	−	0.650691i	$-0.774479\pi$
$617$	−31.8056	+	5.03752i	−1.28045	+	0.202803i	−0.521103	+	0.853494i	$0.674479\pi$
$618$	3.05185	−	11.3897i	0.122764	−	0.458160i
$619$	16.9052	−	7.52667i	0.679476	−	0.302522i	−0.0378261	−	0.999284i	$-0.512043\pi$
$619$	16.9052	−	7.52667i	0.679476	−	0.302522i	0.717302	+	0.696762i	$0.245377\pi$
$620$		0			0
$621$	11.1658	−	25.0789i	0.448069	−	1.00638i
$622$	24.5386	+	3.88654i	0.983910	+	0.155836i
$623$	3.23974	−	27.8702i	0.129797	−	1.11660i
$624$		−	11.8683i		−	0.475111i
$625$		0			0
$626$	18.2402	+	10.5310i	0.729023	+	0.420902i
$627$	3.64598	−	2.36773i	0.145606	−	0.0945578i
$628$	23.9290	−	9.18549i	0.954871	−	0.366541i
$629$	11.4704	−	8.33374i	0.457355	−	0.332288i
$630$		0			0
$631$	20.5730	+	14.9472i	0.818998	+	0.595037i	0.916425	−	0.400206i	$-0.131061\pi$
$631$	20.5730	+	14.9472i	0.818998	+	0.595037i	−0.0974273	+	0.995243i	$0.531061\pi$
$632$	−8.13469	−	2.17968i	−0.323580	−	0.0867031i
$633$	−1.89443	+	4.93515i	−0.0752968	+	0.196155i
$634$	29.3763	−	26.4506i	1.16668	−	1.05049i
$635$		0			0
$636$	0.524836	−	0.170530i	0.0208111	−	0.00676194i
$637$	31.7803	−	4.31887i	1.25918	−	0.171120i
$638$	2.47450	−	1.26082i	0.0979666	−	0.0499165i
$639$	3.53468	+	3.18264i	0.139830	+	0.125903i
$640$		0			0
$641$	25.0351	+	27.8043i	0.988828	+	1.09820i	0.995164	+	0.0982243i	$0.0313163\pi$
$641$	25.0351	+	27.8043i	0.988828	+	1.09820i	−0.00633676	+	0.999980i	$0.502017\pi$
$642$	26.5475	−	21.4978i	1.04775	−	0.848449i
$643$	14.7951	−	14.7951i	0.583460	−	0.583460i	−0.352392	−	0.935852i	$-0.614632\pi$
$643$	14.7951	−	14.7951i	0.583460	−	0.583460i	0.935852	+	0.352392i	$0.114632\pi$
$644$	−27.9180	+	27.3102i	−1.10012	+	1.07617i
$645$		0			0
$646$	21.4678	+	9.55808i	0.844639	+	0.376058i
$647$	16.2665	−	20.0874i	0.639502	−	0.789719i	−0.349608	−	0.936896i	$-0.613685\pi$
$647$	16.2665	−	20.0874i	0.639502	−	0.789719i	0.989110	+	0.147177i	$0.0470187\pi$
$648$	−1.38256	−	2.12896i	−0.0543122	−	0.0836334i
$649$	−3.61080	−	6.25410i	−0.141736	−	0.245495i
$650$		0			0
$651$	−7.79252	−	20.9877i	−0.305413	−	0.822572i
$652$	−11.7898	−	6.00718i	−0.461723	−	0.235259i
$653$	9.42440	+	24.5514i	0.368805	+	0.960770i	0.984904	+	0.173101i	$0.0553788\pi$
$653$	9.42440	+	24.5514i	0.368805	+	0.960770i	−0.616099	+	0.787669i	$0.711288\pi$
$654$	3.47089	+	33.0234i	0.135723	+	1.29132i
$655$		0			0
$656$	−17.3573	−	1.82432i	−0.677687	−	0.0712278i
$657$	2.11712	+	2.11712i	0.0825967	+	0.0825967i
$658$	0.882215	−	1.48993i	0.0343923	−	0.0580836i
$659$	5.69893	+	1.85169i	0.221999	+	0.0721317i	0.417904	−	0.908491i	$-0.362765\pi$
$659$	5.69893	+	1.85169i	0.221999	+	0.0721317i	−0.195906	+	0.980623i	$0.562765\pi$
$660$		0			0
$661$	9.56586	−	45.0038i	0.372069	−	1.75045i	−0.250723	−	0.968059i	$-0.580668\pi$
$661$	9.56586	−	45.0038i	0.372069	−	1.75045i	0.622792	−	0.782387i	$-0.285998\pi$
$662$	64.9671	+	3.40478i	2.52502	+	0.132331i
$663$	4.67520	−	7.19918i	0.181570	−	0.279593i
$664$	0.890129	+	2.73954i	0.0345437	+	0.106315i
$665$		0			0
$666$	9.38224	−	28.8756i	0.363555	−	1.11891i
$667$	4.95344	+	6.11699i	0.191798	+	0.236851i
$668$	6.43627	+	24.0205i	0.249027	+	0.929381i
$669$	4.50498	+	10.1184i	0.174173	+	0.391198i
$670$		0			0
$671$	−3.27395	−	4.50620i	−0.126389	−	0.173960i
$672$	3.49826	+	17.3973i	0.134948	+	0.671114i
$673$	−7.94108	+	15.5853i	−0.306106	+	0.600767i	−0.991899	−	0.127030i	$-0.959456\pi$
$673$	−7.94108	+	15.5853i	−0.306106	+	0.600767i	0.685793	+	0.727797i	$0.259456\pi$
$674$	−63.0398	+	36.3960i	−2.42820	+	1.40192i
$675$		0			0
$676$	9.47819	−	16.4167i	0.364546	−	0.631412i
$677$	34.8733	−	1.82763i	1.34029	−	0.0702417i	0.631344	−	0.775503i	$-0.282504\pi$
$677$	34.8733	−	1.82763i	1.34029	−	0.0702417i	0.708947	+	0.705262i	$0.249170\pi$
$678$	2.37128	−	14.9717i	0.0910685	−	0.574984i
$679$	11.7505	−	5.82520i	0.450943	−	0.223551i
$680$		0			0
$681$	0.421309	−	4.00849i	0.0161446	−	0.153606i
$682$	−21.6081	+	5.78987i	−0.827417	+	0.221706i
$683$	−37.9867	−	14.5817i	−1.45352	−	0.557954i	−0.501817	−	0.864974i	$-0.667335\pi$
$683$	−37.9867	−	14.5817i	−1.45352	−	0.557954i	−0.951703	+	0.307020i	$0.900668\pi$
$684$	26.7039	−	5.67610i	1.02105	−	0.217031i
$685$		0			0
$686$	−36.5897	+	12.6763i	−1.39700	+	0.483985i
$687$	2.52160	+	4.94891i	0.0962049	+	0.188813i
$688$	17.7852	+	11.5498i	0.678053	+	0.440333i
$689$	−1.25537	−	0.266838i	−0.0478260	−	0.0101657i
$690$		0			0
$691$	−3.69969	−	17.4057i	−0.140743	−	0.662144i	−0.990787	−	0.135432i	$-0.956758\pi$
$691$	−3.69969	−	17.4057i	−0.140743	−	0.662144i	0.850044	−	0.526712i	$-0.176575\pi$
$692$	−5.09328	−	32.1577i	−0.193618	−	1.22245i
$693$	−3.71565	−	5.23434i	−0.141146	−	0.198836i
$694$	−33.1078	+	45.5689i	−1.25675	+	1.72977i
$695$		0			0
$696$	−0.811972	+	0.0853417i	−0.0307777	+	0.00323487i
$697$	−9.81012	−	7.94408i	−0.371585	−	0.300903i
$698$	3.16550	+	60.4013i	0.119816	+	2.28622i
$699$	−7.17212			−0.271275
$700$		0			0
$701$	−20.8675			−0.788156			−0.394078	−	0.919077i	$-0.628936\pi$
$701$	−20.8675			−0.788156			−0.394078	+	0.919077i	$0.628936\pi$
$702$	−2.21144	−	42.1969i	−0.0834656	−	1.59262i
$703$	24.3434	+	19.7129i	0.918128	+	0.743485i
$704$	11.1201	−	1.16877i	0.419105	−	0.0440497i
$705$		0			0
$706$	14.3393	−	19.7364i	0.539667	−	0.742788i
$707$	40.0393	−	3.76330i	1.50583	−	0.141533i
$708$	2.11905	+	13.3791i	0.0796387	+	0.502819i
$709$	−0.161305	−	0.758882i	−0.00605795	−	0.0285004i	0.975015	−	0.222140i	$-0.0713041\pi$
$709$	−0.161305	−	0.758882i	−0.00605795	−	0.0285004i	−0.981073	+	0.193639i	$0.937971\pi$
$710$		0			0
$711$	24.4840	+	5.20424i	0.918223	+	0.195174i
$712$	6.91241	+	4.48897i	0.259054	+	0.168231i
$713$	−28.7838	−	56.4913i	−1.07796	−	2.11562i
$714$	−3.82042	+	9.63428i	−0.142976	+	0.360554i
$715$		0			0
$716$	3.73407	−	0.793701i	0.139549	−	0.0296620i
$717$	14.8777	+	5.71101i	0.555618	+	0.213282i
$718$	−8.99106	+	2.40915i	−0.335543	+	0.0899086i
$719$	3.85474	−	36.6754i	0.143757	−	1.36776i	−0.650189	−	0.759773i	$-0.725310\pi$
$719$	3.85474	−	36.6754i	0.143757	−	1.36776i	0.793946	−	0.607988i	$-0.208023\pi$
$720$		0			0
$721$	9.94835	−	14.9562i	0.370496	−	0.556997i
$722$	−1.90712	+	12.0411i	−0.0709755	+	0.448122i
$723$	21.5278	−	1.12822i	0.800628	−	0.0419591i
$724$	4.12478	−	7.14434i	0.153296	−	0.265517i
$725$		0			0
$726$	−14.8859	+	8.59439i	−0.552468	+	0.318968i
$727$	−9.04006	+	17.7421i	−0.335277	+	0.658019i	−0.995676	−	0.0928967i	$-0.970387\pi$
$727$	−9.04006	+	17.7421i	−0.335277	+	0.658019i	0.660398	+	0.750915i	$0.270387\pi$
$728$	−3.00980	+	8.92772i	−0.111551	+	0.330883i
$729$	−2.02583	−	2.78831i	−0.0750307	−	0.103271i
$730$		0			0
$731$	6.23857	+	14.0121i	0.230742	+	0.518254i
$732$	2.70410	+	10.0919i	0.0999466	+	0.373006i
$733$	0.0252173	+	0.0311408i	0.000931422	+	0.00115021i	0.777611	−	0.628745i	$-0.216431\pi$
$733$	0.0252173	+	0.0311408i	0.000931422	+	0.00115021i	−0.776680	+	0.629895i	$0.783098\pi$
$734$	16.5940	−	51.0711i	0.612496	−	1.88507i
$735$		0			0
$736$	15.5297	+	47.7955i	0.572432	+	1.76177i
$737$	−7.02618	+	10.8194i	−0.258813	+	0.398537i
$738$	−26.9947	−	1.41473i	−0.993689	−	0.0520771i
$739$	4.01685	−	18.8978i	0.147762	−	0.695167i	−0.840427	−	0.541925i	$-0.817696\pi$
$739$	4.01685	−	18.8978i	0.147762	−	0.695167i	0.988189	−	0.153241i	$-0.0489712\pi$
$740$		0			0
$741$	18.0366	+	5.86045i	0.662592	+	0.215289i
$742$	1.54947	+	0.0170523i	0.0568829	+	0.000626011i
$743$	−16.7789	−	16.7789i	−0.615557	−	0.615557i	0.328831	−	0.944389i	$-0.393345\pi$
$743$	−16.7789	−	16.7789i	−0.615557	−	0.615557i	−0.944389	+	0.328831i	$0.893345\pi$
$744$	6.54044	+	0.687427i	0.239784	+	0.0252023i
$745$		0			0
$746$	7.82715	+	74.4703i	0.286572	+	2.72655i
$747$	−3.06818	−	7.99289i	−0.112259	−	0.292445i
$748$	5.00597	+	2.55067i	0.183036	+	0.0932617i
$749$	48.7843	−	18.1132i	1.78254	−	0.661840i
$750$		0			0
$751$	−6.63402	−	11.4905i	−0.242079	−	0.419293i	0.719227	−	0.694775i	$-0.244496\pi$
$751$	−6.63402	−	11.4905i	−0.242079	−	0.419293i	−0.961306	+	0.275482i	$0.911163\pi$
$752$	−0.531615	−	0.818615i	−0.0193860	−	0.0298518i
$753$	8.05728	−	9.94991i	0.293623	−	0.362595i
$754$	11.0679	+	4.92773i	0.403068	+	0.179457i
$755$		0			0
$756$	6.86883	+	26.8116i	0.249817	+	0.975130i
$757$	−1.13591	+	1.13591i	−0.0412853	+	0.0412853i	−0.727448	−	0.686163i	$-0.759294\pi$
$757$	−1.13591	+	1.13591i	−0.0412853	+	0.0412853i	0.686163	+	0.727448i	$0.259294\pi$
$758$	36.8879	−	29.8712i	1.33983	−	1.08497i
$759$	3.63330	+	4.03519i	0.131880	+	0.146468i
$760$		0			0
$761$	−23.6079	−	21.2567i	−0.855787	−	0.770554i	0.119187	−	0.992872i	$-0.461971\pi$
$761$	−23.6079	−	21.2567i	−0.855787	−	0.770554i	−0.974974	+	0.222318i	$0.928638\pi$
$762$	20.1050	−	10.2440i	0.728328	−	0.371102i
$763$	−11.0608	+	49.3595i	−0.400427	+	1.78693i
$764$	−6.68717	+	2.17279i	−0.241933	+	0.0786089i
$765$		0			0
$766$	−33.7996	+	30.4333i	−1.22123	+	1.09960i
$767$	11.2899	−	29.4111i	0.407654	−	1.06197i
$768$	6.83311	+	1.83093i	0.246569	+	0.0660679i
$769$	11.1412	+	8.09458i	0.401763	+	0.291898i	0.770259	−	0.637731i	$-0.220127\pi$
$769$	11.1412	+	8.09458i	0.401763	+	0.291898i	−0.368495	+	0.929630i	$0.620127\pi$
$770$		0			0
$771$	−20.5429	+	14.9253i	−0.739834	+	0.537521i
$772$	−37.7451	+	14.4890i	−1.35848	+	0.521470i
$773$	8.42289	−	5.46989i	0.302950	−	0.196738i	−0.384207	−	0.923247i	$-0.625525\pi$
$773$	8.42289	−	5.46989i	0.302950	−	0.196738i	0.687157	+	0.726509i	$0.258858\pi$
$774$	28.4449	+	16.4227i	1.02243	+	0.590302i
$775$		0			0
$776$			3.85263i			0.138301i
$777$	−8.24280	+	11.0866i	−0.295709	+	0.397729i
$778$	26.8433	+	4.25155i	0.962377	+	0.152426i
$779$	11.3434	−	25.4776i	0.406418	−	0.912830i
$780$		0			0
$781$	−1.97561	+	0.879597i	−0.0706928	+	0.0314745i
$782$	−7.59663	+	28.3510i	−0.271655	+	1.01383i
$783$	5.50947	−	0.872614i	0.196892	−	0.0311847i
$784$	−2.75896	+	21.6538i	−0.0985341	+	0.773349i
$785$		0			0
$786$	4.11711	−	4.57252i	0.146853	−	0.163096i
$787$	−1.12669	+	21.4984i	−0.0401620	+	0.766337i	0.902114	+	0.431499i	$0.142015\pi$
$787$	−1.12669	+	21.4984i	−0.0401620	+	0.766337i	−0.942276	+	0.334838i	$0.891318\pi$
$788$	2.40250	−	45.8425i	0.0855856	−	1.63307i
$789$	−0.226612	+	0.251678i	−0.00806760	+	0.00895998i
$790$		0			0
$791$	10.7091	−	20.4581i	0.380773	−	0.727407i
$792$	1.86241	−	0.294977i	0.0661779	−	0.0104815i
$793$	6.28891	−	23.4705i	0.223326	−	0.833463i
$794$	−9.12721	+	4.06369i	−0.323912	+	0.144215i
$795$		0			0
$796$	−0.185104	+	0.415750i	−0.00656084	+	0.0147359i
$797$	−5.20937	−	0.825084i	−0.184526	−	0.0292260i	0.0634877	−	0.997983i	$-0.479778\pi$
$797$	−5.20937	−	0.825084i	−0.184526	−	0.0292260i	−0.248013	+	0.968757i	$0.579778\pi$
$798$	−22.7444	−	2.64390i	−0.805144	−	0.0935931i
$799$		−	0.705981i		−	0.0249758i
$800$		0			0
$801$	−21.2154	−	12.2487i	−0.749608	−	0.432786i
$802$	26.5961	−	17.2717i	0.939140	−	0.609885i
$803$	−1.27088	+	0.487846i	−0.0448485	+	0.0172157i
$804$	19.5768	−	14.2234i	0.690422	−	0.501621i
$805$		0			0
$806$	−78.9508	−	57.3611i	−2.78092	−	2.02046i
$807$	−15.3680	−	4.11784i	−0.540979	−	0.144955i
$808$	−4.23359	+	11.0289i	−0.148937	+	0.387995i
$809$	6.16004	−	5.54653i	0.216575	−	0.195005i	−0.553701	−	0.832716i	$-0.686785\pi$
$809$	6.16004	−	5.54653i	0.216575	−	0.195005i	0.770276	+	0.637710i	$0.220118\pi$
$810$		0			0
$811$	−22.9445	+	7.45511i	−0.805689	+	0.261784i	−0.682771	−	0.730632i	$-0.739225\pi$
$811$	−22.9445	+	7.45511i	−0.805689	+	0.261784i	−0.122918	+	0.992417i	$0.539225\pi$
$812$	−7.74365	−	1.73524i	−0.271749	−	0.0608951i
$813$	−14.2891	+	7.28065i	−0.501140	+	0.255343i
$814$	10.2587	+	9.23695i	0.359566	+	0.323755i
$815$		0			0
$816$	3.90932	+	4.34174i	0.136854	+	0.151991i
$817$	−26.3349	+	21.3255i	−0.921340	+	0.746087i
$818$	−15.1952	+	15.1952i	−0.531288	+	0.531288i
$819$	7.54481	−	26.9670i	0.263637	−	0.942303i
$820$		0			0
$821$	10.2681	+	4.57166i	0.358359	+	0.159552i	0.578016	−	0.816025i	$-0.303827\pi$
$821$	10.2681	+	4.57166i	0.358359	+	0.159552i	−0.219657	+	0.975577i	$0.570494\pi$
$822$	8.27902	−	10.2237i	0.288764	−	0.356594i
$823$	−9.34851	−	14.3955i	−0.325869	−	0.501794i	0.637327	−	0.770593i	$-0.280040\pi$
$823$	−9.34851	−	14.3955i	−0.325869	−	0.501794i	−0.963196	+	0.268799i	$0.913373\pi$
$824$	2.63830	+	4.56967i	0.0919096	+	0.159192i
$825$		0			0
$826$	−6.36329	+	37.5005i	−0.221407	+	1.30481i
$827$	20.7397	+	10.5674i	0.721190	+	0.367465i	0.775745	−	0.631046i	$-0.217374\pi$
$827$	20.7397	+	10.5674i	0.721190	+	0.367465i	−0.0545555	+	0.998511i	$0.517374\pi$
$828$	12.2199	+	31.8339i	0.424671	+	1.10630i
$829$	2.64740	+	25.1883i	0.0919480	+	0.874827i	0.939139	+	0.343538i	$0.111625\pi$
$829$	2.64740	+	25.1883i	0.0919480	+	0.874827i	−0.847191	+	0.531289i	$0.821708\pi$
$830$		0			0
$831$	6.31767	+	0.664014i	0.219157	+	0.0230344i
$832$	34.4910	+	34.4910i	1.19576	+	1.19576i
$833$	−10.2035	+	12.0482i	−0.353531	+	0.417445i
$834$	14.6044	+	4.74526i	0.505710	+	0.164315i
$835$		0			0
$836$	−2.58073	+	12.1414i	−0.0892565	+	0.419919i
$837$	−44.8703	−	2.35155i	−1.55095	−	0.0812816i
$838$	20.3893	−	31.3967i	0.704335	−	1.08458i
$839$	17.1783	+	52.8695i	0.593062	+	1.82526i	0.564144	+	0.825677i	$0.309206\pi$
$839$	17.1783	+	52.8695i	0.593062	+	1.82526i	0.0289189	+	0.999582i	$0.490794\pi$
$840$		0			0
$841$	8.46726	−	26.0596i	0.291975	−	0.898605i
$842$	−22.0978	−	27.2885i	−0.761540	−	0.940424i
$843$	4.02417	+	15.0184i	0.138600	+	0.517261i
$844$	−6.13909	−	13.7886i	−0.211316	−	0.474624i
$845$		0			0
$846$	−0.888617	−	1.22308i	−0.0305513	−	0.0420502i
$847$	−25.6709	+	5.16193i	−0.882062	+	0.177366i
$848$	0.396565	−	0.778302i	0.0136181	−	0.0267270i
$849$	2.04998	−	1.18355i	0.0703550	−	0.0406195i
$850$		0			0
$851$	−19.5621	+	33.8826i	−0.670581	+	1.16148i
$852$	4.05088	−	0.212298i	0.138781	−	0.00727319i
$853$	6.62710	−	41.8419i	0.226908	−	1.43264i	−0.566557	−	0.824023i	$-0.691725\pi$
$853$	6.62710	−	41.8419i	0.226908	−	1.43264i	0.793465	−	0.608616i	$-0.208275\pi$
$854$	−1.85770	+	29.2784i	−0.0635693	+	1.00189i
$855$		0			0
$856$	−1.59787	+	15.2028i	−0.0546142	+	0.519620i
$857$	36.7601	−	9.84983i	1.25570	−	0.336464i	0.431164	−	0.902274i	$-0.358103\pi$
$857$	36.7601	−	9.84983i	1.25570	−	0.336464i	0.824536	+	0.565810i	$0.191436\pi$
$858$	7.80261	+	2.99514i	0.266377	+	0.102252i
$859$	−50.1863	+	10.6674i	−1.71233	+	0.363968i	−0.956711	−	0.291040i	$-0.905999\pi$
$859$	−50.1863	+	10.6674i	−1.71233	+	0.363968i	−0.755622	+	0.655008i	$0.772665\pi$
$860$		0			0
$861$	11.4338	+	4.53401i	0.389663	+	0.154519i
$862$	8.49088	+	16.6643i	0.289200	+	0.567588i
$863$	18.3280	+	11.9023i	0.623893	+	0.405161i	0.817508	−	0.575917i	$-0.195355\pi$
$863$	18.3280	+	11.9023i	0.623893	+	0.405161i	−0.193616	+	0.981077i	$0.562021\pi$
$864$	34.8369	+	7.40481i	1.18517	+	0.251917i
$865$		0			0
$866$	7.66009	+	36.0379i	0.260300	+	1.22462i
$867$	−1.54799	−	9.77363i	−0.0525725	−	0.331930i
$868$	58.1060	+	26.6404i	1.97224	+	0.904236i
$869$	−6.68946	+	9.20725i	−0.226924	+	0.312334i
$870$		0			0
$871$	−55.9695	+	5.88263i	−1.89645	+	0.199325i
$872$	−11.5477	−	9.35116i	−0.391055	−	0.316670i
$873$	−0.599293	−	11.4352i	−0.0202830	−	0.387023i
$874$	−64.8458			−2.19344
$875$		0			0
$876$	2.55345			0.0862732
$877$	−0.0741129	−	1.41416i	−0.00250261	−	0.0477527i	0.997093	−	0.0761974i	$-0.0242779\pi$
$877$	−0.0741129	−	1.41416i	−0.00250261	−	0.0477527i	−0.999595	+	0.0284446i	$0.990945\pi$
$878$	−44.5280	−	36.0580i	−1.50275	−	1.21690i
$879$	0.683387	−	0.0718269i	0.0230501	−	0.00242266i
$880$		0			0
$881$	5.05676	−	6.96003i	0.170367	−	0.234489i	−0.715293	−	0.698825i	$-0.753707\pi$
$881$	5.05676	−	6.96003i	0.170367	−	0.234489i	0.885659	+	0.464335i	$0.153707\pi$
$882$	−2.51208	+	33.7160i	−0.0845860	+	1.13528i
$883$	−6.37108	−	40.2254i	−0.214404	−	1.35369i	−0.826512	−	0.562919i	$-0.809678\pi$
$883$	−6.37108	−	40.2254i	−0.214404	−	1.35369i	0.612108	−	0.790774i	$-0.290322\pi$
$884$	5.09580	+	23.9739i	0.171390	+	0.806328i
$885$		0			0
$886$	22.6684	+	4.81832i	0.761561	+	0.161875i
$887$	20.8067	+	13.5120i	0.698619	+	0.453689i	0.844459	−	0.535619i	$-0.179922\pi$
$887$	20.8067	+	13.5120i	0.698619	+	0.453689i	−0.145840	+	0.989308i	$0.546589\pi$
$888$	−1.84240	−	3.61591i	−0.0618269	−	0.121342i
$889$	34.0076	−	5.00330i	1.14058	−	0.167805i
$890$		0			0
$891$	−3.35549	+	0.713231i	−0.112413	+	0.0238941i
$892$	−29.5239	−	11.3331i	−0.988532	−	0.379462i
$893$	1.50658	−	0.403688i	0.0504159	−	0.0135089i
$894$	0.319632	−	3.04109i	0.0106901	−	0.101709i
$895$		0			0
$896$	−13.4603	−	8.95336i	−0.449678	−	0.299111i
$897$	−3.70552	+	23.3957i	−0.123724	+	0.781160i
$898$	−83.7609	+	4.38972i	−2.79514	+	0.146487i
$899$	6.44144	−	11.1569i	0.214834	−	0.372103i
$900$		0			0
$901$	0.547146	−	0.315895i	0.0182281	−	0.0105240i
$902$	5.57975	−	10.9509i	0.185785	−	0.364624i
$903$	−9.87750	−	11.2159i	−0.328703	−	0.373241i
$904$	3.98709	+	5.48776i	0.132609	+	0.182520i
$905$		0			0
$906$	4.42892	+	9.94752i	0.147141	+	0.330484i
$907$	8.07670	+	30.1426i	0.268182	+	1.00087i	0.960274	+	0.279060i	$0.0900229\pi$
$907$	8.07670	+	30.1426i	0.268182	+	1.00087i	−0.692091	+	0.721810i	$0.743310\pi$
$908$	7.24236	+	8.94357i	0.240346	+	0.296803i
$909$	10.8504	−	33.3940i	0.359883	−	1.10761i
$910$		0			0
$911$	−11.4702	−	35.3017i	−0.380025	−	1.16960i	−0.940025	−	0.341105i	$-0.889199\pi$
$911$	−11.4702	−	35.3017i	−0.380025	−	1.16960i	0.560000	−	0.828492i	$-0.310801\pi$
$912$	−7.03001	+	10.8253i	−0.232787	+	0.358460i
$913$	3.88732	+	0.203726i	0.128651	+	0.00674234i
$914$	−14.7720	+	69.4967i	−0.488614	+	2.29875i
$915$		0			0
$916$	−15.0826	−	4.90064i	−0.498344	−	0.161922i
$917$	8.16845	−	4.59695i	0.269746	−	0.151805i
$918$	14.7084	+	14.7084i	0.485448	+	0.485448i
$919$	42.2670	+	4.44244i	1.39426	+	0.146543i	0.771678	−	0.636013i	$-0.219417\pi$
$919$	42.2670	+	4.44244i	1.39426	+	0.146543i	0.622581	+	0.782555i	$0.286084\pi$
$920$		0			0
$921$	−1.27711	−	12.1509i	−0.0420822	−	0.400385i
$922$	−23.6756	−	61.6771i	−0.779715	−	2.03123i
$923$	−8.40577	−	4.28295i	−0.276679	−	0.140975i
$924$	−5.39729	−	0.915841i	−0.177558	−	0.0301290i
$925$		0			0
$926$	19.9093	+	34.4838i	0.654259	+	1.13321i
$927$	−8.54171	−	13.1531i	−0.280546	−	0.432004i
$928$	−6.42635	+	7.93588i	−0.210955	+	0.260508i
$929$	−13.8640	−	6.17267i	−0.454864	−	0.202519i	0.166498	−	0.986042i	$-0.446754\pi$
$929$	−13.8640	−	6.17267i	−0.454864	−	0.202519i	−0.621363	+	0.783523i	$0.713421\pi$
$930$		0			0
$931$	−31.5457	−	14.8853i	−1.03387	−	0.487848i
$932$	14.4802	−	14.4802i	0.474315	−	0.474315i
$933$	−7.67057	+	6.21151i	−0.251123	+	0.203356i
$934$	8.33650	+	9.25862i	0.272778	+	0.302951i
$935$		0			0
$936$	6.11301	+	5.50418i	0.199810	+	0.179910i
$937$	−22.2665	+	11.3453i	−0.727415	+	0.370636i	−0.778152	−	0.628076i	$-0.783843\pi$
$937$	−22.2665	+	11.3453i	−0.727415	+	0.370636i	0.0507375	+	0.998712i	$0.483843\pi$
$938$	64.8497	−	20.2847i	2.11742	−	0.662319i
$939$	−7.95790	+	2.58568i	−0.259696	+	0.0843805i
$940$		0			0
$941$	12.3945	−	11.1600i	0.404049	−	0.363807i	−0.441906	−	0.897061i	$-0.645698\pi$
$941$	12.3945	−	11.1600i	0.404049	−	0.363807i	0.845955	+	0.533254i	$0.179031\pi$
$942$	−6.72646	+	17.5230i	−0.219160	+	0.570931i
$943$	33.6465	+	9.01555i	1.09568	+	0.293587i
$944$	17.3467	+	12.6031i	0.564586	+	0.410196i
$945$		0			0
$946$	−12.0816	+	8.77782i	−0.392808	+	0.285392i
$947$	−22.3303	+	8.57180i	−0.725637	+	0.278546i	−0.693017	−	0.720922i	$-0.743719\pi$
$947$	−22.3303	+	8.57180i	−0.725637	+	0.278546i	−0.0326209	+	0.999468i	$0.510385\pi$
$948$	17.9035	−	11.6267i	0.581478	−	0.377617i
$949$	−5.14293	−	2.96927i	−0.166947	−	0.0963866i
$950$		0			0
$951$			15.7043i			0.509247i
$952$	−1.83966	−	4.25742i	−0.0596236	−	0.137984i
$953$	−52.6232	−	8.33470i	−1.70463	−	0.269987i	−0.773270	−	0.634077i	$-0.781380\pi$
$953$	−52.6232	−	8.33470i	−1.70463	−	0.269987i	−0.931364	+	0.364090i	$0.881380\pi$
$954$	0.550286	−	1.23596i	0.0178162	−	0.0400158i
$955$		0			0
$956$	−41.5677	+	18.5071i	−1.34440	+	0.598563i
$957$	−0.285561	+	1.06573i	−0.00923086	+	0.0344500i
$958$	−43.0597	+	6.81999i	−1.39120	+	0.220344i
$959$	16.9265	−	10.7293i	0.546586	−	0.346466i
$960$		0			0
$961$	−48.6936	+	54.0798i	−1.57076	+	1.74451i
$962$	−3.15169	+	60.1379i	−0.101615	+	1.93892i
$963$	2.37788	−	45.3726i	0.0766261	−	1.46211i
$964$	−41.1858	+	45.7415i	−1.32651	+	1.47323i
$965$		0			0
$966$	−1.18239	−	28.5749i	−0.0380429	−	0.919384i
$967$	31.4763	−	4.98535i	1.01221	−	0.160318i	0.371768	−	0.928326i	$-0.378752\pi$
$967$	31.4763	−	4.98535i	1.01221	−	0.160318i	0.640441	+	0.768008i	$0.278752\pi$
$968$	1.99080	−	7.42978i	0.0639868	−	0.238802i
$969$	−8.52869	+	3.79722i	−0.273981	+	0.121984i
$970$		0			0
$971$	−15.7478	+	35.3701i	−0.505370	+	1.13508i	0.463180	+	0.886264i	$0.346708\pi$
$971$	−15.7478	+	35.3701i	−0.505370	+	1.13508i	−0.968551	+	0.248816i	$0.919958\pi$
$972$	37.3524	+	5.91604i	1.19808	+	0.189757i
$973$	18.7727	+	13.9573i	0.601824	+	0.447451i
$974$		−	61.3676i		−	1.96634i
$975$		0			0
$976$	14.3221	+	8.26889i	0.458441	+	0.264681i
$977$	−24.2449	+	15.7448i	−0.775663	+	0.503721i	−0.870737	−	0.491749i	$-0.836358\pi$
$977$	−24.2449	+	15.7448i	−0.775663	+	0.503721i	0.0950743	+	0.995470i	$0.469691\pi$
$978$	9.04607	−	3.47246i	0.289261	−	0.111037i
$979$	9.01096	−	6.54684i	0.287991	−	0.209238i
$980$		0			0
$981$	35.7300	+	25.9594i	1.14077	+	0.828818i
$982$	36.3639	+	9.74367i	1.16042	+	0.310933i
$983$	3.50625	−	9.13410i	0.111832	−	0.291332i	−0.866230	−	0.499645i	$-0.833464\pi$
$983$	3.50625	−	9.13410i	0.111832	−	0.291332i	0.978062	+	0.208313i	$0.0667971\pi$
$984$	−2.68510	+	2.41768i	−0.0855979	+	0.0770727i
$985$		0			0
$986$	−5.67209	+	1.84297i	−0.180636	+	0.0586922i
$987$	0.205360	+	0.656531i	0.00653669	+	0.0208976i
$988$	−48.2471	+	24.5831i	−1.53494	+	0.782093i
$989$	−31.4535	−	28.3209i	−1.00016	−	0.900552i
$990$		0			0
$991$	−16.3474	−	18.1556i	−0.519291	−	0.576732i	0.425270	−	0.905067i	$-0.360179\pi$
$991$	−16.3474	−	18.1556i	−0.519291	−	0.576732i	−0.944561	+	0.328335i	$0.893513\pi$
$992$	63.9235	−	51.7642i	2.02957	−	1.64352i
$993$	−18.2755	+	18.2755i	−0.579955	+	0.579955i
$994$	10.9691	+	3.06894i	0.347920	+	0.0973408i
$995$		0			0
$996$	−6.67037	−	2.96984i	−0.211359	−	0.0941030i
$997$	−13.7449	+	16.9735i	−0.435305	+	0.537556i	−0.946840	−	0.321706i	$-0.895744\pi$
$997$	−13.7449	+	16.9735i	−0.435305	+	0.537556i	0.511535	+	0.859262i	$0.329077\pi$
$998$	6.05710	+	9.32712i	0.191734	+	0.295245i
$999$	13.8634	+	24.0121i	0.438619	+	0.759710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.143.3		288
5.2	odd	4		875.2.bb.c.857.16		288
5.3	odd	4		175.2.x.a.17.3	yes	288
5.4	even	2		875.2.bb.b.143.16		288
7.5	odd	6	inner	875.2.bb.a.768.3		288
25.3	odd	20		875.2.bb.b.507.16		288
25.4	even	10		175.2.x.a.3.16	✓	288
25.21	even	5		875.2.bb.c.493.3		288
25.22	odd	20	inner	875.2.bb.a.507.3		288
35.12	even	12		875.2.bb.c.607.3		288
35.19	odd	6		875.2.bb.b.768.16		288
35.33	even	12		175.2.x.a.117.16	yes	288
175.47	even	60	inner	875.2.bb.a.257.3		288
175.54	odd	30		175.2.x.a.103.3	yes	288
175.96	odd	30		875.2.bb.c.243.16		288
175.103	even	60		875.2.bb.b.257.16		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.16	✓	288	25.4	even	10
175.2.x.a.17.3	yes	288	5.3	odd	4
175.2.x.a.103.3	yes	288	175.54	odd	30
175.2.x.a.117.16	yes	288	35.33	even	12
875.2.bb.a.143.3		288	1.1	even	1	trivial
875.2.bb.a.257.3		288	175.47	even	60	inner
875.2.bb.a.507.3		288	25.22	odd	20	inner
875.2.bb.a.768.3		288	7.5	odd	6	inner
875.2.bb.b.143.16		288	5.4	even	2
875.2.bb.b.257.16		288	175.103	even	60
875.2.bb.b.507.16		288	25.3	odd	20
875.2.bb.b.768.16		288	35.19	odd	6
875.2.bb.c.243.16		288	175.96	odd	30
875.2.bb.c.493.3		288	25.21	even	5
875.2.bb.c.607.3		288	35.12	even	12
875.2.bb.c.857.16		288	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.109427 - 2.08800i) q^{2} +(0.645540 + 0.522748i) q^{3} +(-2.35872 + 0.247911i) q^{4} +(1.02086 - 1.40509i) q^{6} +(2.15744 - 1.53148i) q^{7} +(0.121581 + 0.767632i) q^{8} +(-0.480279 - 2.25953i) q^{9} +(1.02734 + 0.218367i) q^{11} +(-1.65224 - 1.07298i) q^{12} +(2.08008 + 4.08239i) q^{13} +(-3.43382 - 4.33715i) q^{14} +(-3.05026 + 0.648353i) q^{16} +(-2.10566 - 0.808289i) q^{17} +(-4.66535 + 1.25008i) q^{18} +(0.520869 - 4.95574i) q^{19} +(2.19329 + 0.139164i) q^{21} +(0.343531 - 2.16897i) q^{22} +(6.21536 - 0.325733i) q^{23} +(-0.322792 + 0.559093i) q^{24} +(8.29642 - 4.78994i) q^{26} +(2.00245 - 3.93004i) q^{27} +(-4.70913 + 4.14720i) q^{28} +(0.743348 + 1.02313i) q^{29} +(-4.14336 - 9.30613i) q^{31} +(2.08985 + 7.79943i) q^{32} +(0.549035 + 0.678002i) q^{33} +(-1.45729 + 4.48507i) q^{34} +(1.69301 + 5.21054i) q^{36} +(-3.42368 + 5.27200i) q^{37} +(-10.4046 - 0.545281i) q^{38} +(-0.791286 + 3.72271i) q^{39} +(5.32280 + 1.72948i) q^{41} +(0.0505673 - 4.59482i) q^{42} +(-4.80861 - 4.80861i) q^{43} +(-2.47733 - 0.260378i) q^{44} +(-1.36026 - 12.9420i) q^{46} +(0.112172 + 0.292218i) q^{47} +(-2.30799 - 1.17598i) q^{48} +(2.30911 - 6.60818i) q^{49} +(-0.936759 - 1.62251i) q^{51} +(-5.91841 - 9.11355i) q^{52} +(-0.176281 + 0.217690i) q^{53} +(-8.42504 - 3.75107i) q^{54} +(1.43792 + 1.46992i) q^{56} +(2.92684 - 2.92684i) q^{57} +(2.05495 - 1.66407i) q^{58} +(-4.60084 - 5.10975i) q^{59} +(-3.94111 - 3.54859i) q^{61} +(-18.9778 + 9.66967i) q^{62} +(-4.49661 - 4.13927i) q^{63} +(10.1249 - 3.28979i) q^{64} +(1.35559 - 1.22058i) q^{66} +(-4.40181 + 11.4671i) q^{67} +(5.16706 + 1.38451i) q^{68} +(4.18254 + 3.03879i) q^{69} +(-1.66579 + 1.21027i) q^{71} +(1.67610 - 0.643393i) q^{72} +(-1.08702 + 0.705919i) q^{73} +(11.3826 + 6.57173i) q^{74} +11.8183i q^{76} +(2.55084 - 1.10223i) q^{77} +(7.85959 + 1.24484i) q^{78} +(-4.40735 + 9.89907i) q^{79} +(-2.98382 + 1.32848i) q^{81} +(3.02870 - 11.3033i) q^{82} +(3.66064 - 0.579789i) q^{83} +(-5.20787 + 0.215495i) q^{84} +(-9.51417 + 10.5666i) q^{86} +(-0.0549787 + 1.04906i) q^{87} +(-0.0427210 + 0.815165i) q^{88} +(7.09604 - 7.88095i) q^{89} +(10.7398 + 5.62191i) q^{91} +(-14.5795 + 2.30917i) q^{92} +(2.19006 - 8.17341i) q^{93} +(0.597877 - 0.266192i) q^{94} +(-2.72805 + 6.12730i) q^{96} +(4.89604 + 0.775456i) q^{97} +(-14.0505 - 4.09830i) q^{98} -2.42618i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more